diff --git a/1_data_computations_with_numpy/.ipynb_checkpoints/1 Intro to NumPy for Data Computation-checkpoint.ipynb b/1_data_computations_with_numpy/.ipynb_checkpoints/1 Intro to NumPy for Data Computation-checkpoint.ipynb
deleted file mode 100644
index 968f1e4..0000000
--- a/1_data_computations_with_numpy/.ipynb_checkpoints/1 Intro to NumPy for Data Computation-checkpoint.ipynb	
+++ /dev/null
@@ -1,3495 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "Od0BVxJyFiMZ"
-   },
-   "source": [
-    "<a name='0'></a>\n",
-    "# Intro to NumPy for Data Computations\n",
-    "\n",
-    "This is lab is performing data computations with NumPy. NumPy is a scientific tool used to make mathematical computations easily. \n",
-    "\n",
-    "In this lab, you will learn to:\n",
-    "\n",
-    " * [1. Create a NumPy array](#1)\n",
-    " * [2. Select data: indexing and slicing of array](#2)\n",
-    " * [3. Perform mathematical and other basic operations](#3)\n",
-    " * [4. Perform basic statistics](#4)\n",
-    " * [5. Manipulate data](#5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "2MG9Fii1d8Wy"
-   },
-   "source": [
-    "If you are using Google Colab, we do not need to install NumPy. We will only have to import it just like this:\n",
-    "\n",
-    "`import numpy as np`\n",
-    "\n",
-    "If you are using local Jupyter notebooks, make sure you have it installed already."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "XzRyETjqGuLE"
-   },
-   "source": [
-    "<a name='1'></a>\n",
-    "## 1. Creating an Array in NumPy\n",
-    "\n",
-    "Array can either be vector or matrice. A vector is one dimensional array, and a matrix is a two or more dimensional array. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {
-    "id": "rFx8BN4bfTWL"
-   },
-   "outputs": [],
-   "source": [
-    "## Importing numpy\n",
-    "\n",
-    "import numpy as np"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "tO9qq2UEGx6M",
-    "outputId": "490647a5-f8fb-4459-eeba-d3657d998afa"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 2, 3, 4, 5])"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Creating a simple 1 dimensional array: vector\n",
-    "np.array([1,2,3,4,5])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "o27WSEaWetl6",
-    "outputId": "3b3406cf-31f1-483f-c0f8-0715dabf5e01"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[ 1,  2,  3,  4,  5],\n",
-       "       [ 6,  7,  8,  9, 10]])"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Creating 2 dimensional array: matrix\n",
-    "\n",
-    "np.array([(1,2,3,4,5), (6,7,8,9,10)])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "m9sI1bT0fjMK",
-    "outputId": "c521c0c5-aba9-40da-aa51-ccd51e11a967"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 2, 3, 4, 5])"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Creating an array from a list\n",
-    "\n",
-    "num_list = [1,2,3,4,5]\n",
-    "\n",
-    "np.array(num_list)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Jo2YqycbgiHV",
-    "outputId": "fb8b61f7-5a05-46d3-e688-ea82991deb2d"
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[1 2 3 4 5]\n"
-     ]
-    }
-   ],
-   "source": [
-    "print(np.array(num_list))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "FWI8bsvmgXfs"
-   },
-   "source": [
-    "### 1.1 Generating Array\n",
-    "\n",
-    "NumPy offers various options to generate an array depending on particular need, such as:\n",
-    "\n",
-    "* Generating identity array\n",
-    "* Generating zero array of a given size\n",
-    "* Generating ones array with a given size\n",
-    "* Generating an array in a given range\n",
-    "* Generating an array with random values\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "OTjgeBrzaDQl",
-    "outputId": "2a2fd24e-5faf-4d51-c450-0249377a9842"
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[1. 0. 0. 0.]\n",
-      " [0. 1. 0. 0.]\n",
-      " [0. 0. 1. 0.]\n",
-      " [0. 0. 0. 1.]]\n"
-     ]
-    }
-   ],
-   "source": [
-    "## Generating an identity array \n",
-    "\n",
-    "identity_array = np.identity(4)\n",
-    "print(identity_array)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "yIt4o9lBgZqo",
-    "outputId": "6632591d-0203-433c-ba07-2376d8b25790"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1., 0., 0., 0.],\n",
-       "       [0., 1., 0., 0.],\n",
-       "       [0., 0., 1., 0.],\n",
-       "       [0., 0., 0., 1.]])"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Generating an identity matrix of 1s\n",
-    "\n",
-    "np.eye(4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Bo3PEZahhnGl",
-    "outputId": "903bfb68-772e-473f-9c7b-9c8461a1a7bf"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[7., 0., 0., 0.],\n",
-       "       [0., 7., 0., 0.],\n",
-       "       [0., 0., 7., 0.],\n",
-       "       [0., 0., 0., 7.]])"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# You can multiply with any constant\n",
-    "\n",
-    "np.eye(4) * 7"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "4yZIO0FWhzv7",
-    "outputId": "15ad3530-0084-4c15-a356-42addb755332"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0., 0., 0., 0., 0.])"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# Generating zero array of a given size\n",
-    "# 1 dimensional zero array\n",
-    "np.zeros(5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Ys3edWPOigeX",
-    "outputId": "4017496b-ffd9-443a-fa1c-ae167ff817ac"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[0., 0., 0., 0., 0., 0.],\n",
-       "       [0., 0., 0., 0., 0., 0.],\n",
-       "       [0., 0., 0., 0., 0., 0.],\n",
-       "       [0., 0., 0., 0., 0., 0.],\n",
-       "       [0., 0., 0., 0., 0., 0.]])"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# Creating two dimensional array: pass the tuple of rows and columns' number\n",
-    "#np.zeros((rows, columns))\n",
-    "\n",
-    "np.zeros((5,6))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "l5hEgxuYiphg",
-    "outputId": "f35fae1f-9cf3-44ee-bff2-9444e4aa28ae"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1., 1., 1., 1., 1.])"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# Generating ones array of a given size\n",
-    "# 1 dimensional one array\n",
-    "\n",
-    "np.ones(5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "S9Tb6tjgjNIW",
-    "outputId": "8216c53d-f9e6-48f7-b106-2f7a71851ac0"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1., 1., 1., 1., 1., 1.],\n",
-       "       [1., 1., 1., 1., 1., 1.],\n",
-       "       [1., 1., 1., 1., 1., 1.],\n",
-       "       [1., 1., 1., 1., 1., 1.],\n",
-       "       [1., 1., 1., 1., 1., 1.]])"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# Creating two dimensional ones array: pass the tuple of rows and columns' number\n",
-    "# np.ones((rows, columns))\n",
-    "\n",
-    "np.ones((5,6))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "iB2v6pfLjWIG",
-    "outputId": "dfe3950c-8b34-48c1-8af9-27dbc48a3af3"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4])"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Generating an array in a given range or interval\n",
-    "\n",
-    "np.arange(0,5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "IldBA00wjrMc",
-    "outputId": "68416c4e-5f56-4a48-df21-b62a767088b9"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0,  2,  4,  6,  8, 10, 12, 14, 16, 18])"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## If you want to control the step size\n",
-    "\n",
-    "np.arange(0,20,2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "kXJAdbO3j1Fv",
-    "outputId": "f278ab62-d48e-4fda-b834-ca7570047ab5"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0.,  5., 10., 15., 20.])"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## You can also use linspace to generate an evenly spaced numbers in a given interval\n",
-    "\n",
-    "np.linspace(0,20,5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "m7wEgM3LkMD7",
-    "outputId": "1b3fb3cd-c3d6-4596-e4c6-c91f21de6f73"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([  0.,  25.,  50.,  75., 100.])"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "\n",
-    "np.linspace(0,100,5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Gk1TCkP_kRKM",
-    "outputId": "1e1075c2-47dc-4abd-a784-5d9fb88f7802"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0.        ,  1.11111111,  2.22222222,  3.33333333,  4.44444444,\n",
-       "        5.55555556,  6.66666667,  7.77777778,  8.88888889, 10.        ])"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.linspace(0,10,10)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "422VmvKLkUIm",
-    "outputId": "3805deac-07ae-4d18-b478-e44ba12305d8"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0.68944519, 0.25872307, 0.7565542 , 0.68606423])"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Generating an array with random values\n",
-    "# Create a 1D array with 4 random numbers\n",
-    "\n",
-    "np.random.rand(4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "_In_Ydv-kt_j",
-    "outputId": "735b1c2e-da13-414e-d773-a56d20745ef7"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0.41979127, 0.83292096, 0.50330078, 0.17331376])"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.random.rand(4)\n",
-    "\n",
-    "#We will not get teh same values"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "EYopwsICk9ZI",
-    "outputId": "1c07d1f3-41bd-47cf-dac7-47f36a158666"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[0.88627071, 0.55624758, 0.97198928, 0.74128787, 0.02940347],\n",
-       "       [0.05604389, 0.22823893, 0.52886436, 0.91998249, 0.01327729],\n",
-       "       [0.74984196, 0.00163448, 0.08632411, 0.08515202, 0.70213274],\n",
-       "       [0.67293052, 0.18162822, 0.38745748, 0.42938446, 0.56581595]])"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.random.rand(4,5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "6achS2SnlLg6",
-    "outputId": "974f6af6-0fa5-4e1d-f0ab-3c8b85514c78"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "27"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### Generate one random integer in a given range\n",
-    "\n",
-    "np.random.randint(5,50)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "a9WGTceNlmxi",
-    "outputId": "ccd0a4ca-94e2-4249-81d7-c40d4eb1e992"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 6, 44, 15,  7, 34, 32, 38, 20, 16, 27])"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### Generate 10 random integers in a given range\n",
-    "\n",
-    "np.random.randint(5,50,10)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Nkz5qtZ2oUFt",
-    "outputId": "f57e0bae-268a-4a8c-8dba-6d6e89ecb971"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "41"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Random see to output the same random vaues at all run time \n",
-    "import random\n",
-    "\n",
-    "random.seed(10)\n",
-    "\n",
-    "random.randint(5,50)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "k67GJ1K0NDU4"
-   },
-   "source": [
-    "<a name='2'></a>\n",
-    "## 2. Data Selection: Indexing and slicing an Array\n",
-    "\n",
-    "Indexing: Selecting individual elements from the array\n",
-    "\n",
-    "Slicing: Selecting group of element from the array. "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "523qanvFjFD6"
-   },
-   "source": [
-    "\n",
-    "### 2.1 1D Array Indexing and Selection"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {
-    "id": "HEi3p6K5NWqn"
-   },
-   "outputs": [],
-   "source": [
-    "# Creating a 1 dimensional vector\n",
-    "\n",
-    "array_1d = np.array([1,2,3,4,5])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "osAwL_bjNqUa",
-    "outputId": "00bd8764-37cd-43cd-b713-4ad2fd7d4947"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Indexing: selcting an element from an array\n",
-    "\n",
-    "array_1d[1]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "g0CV4DR4Pxrr",
-    "outputId": "03054ff3-f802-41d6-ed9a-948f00d67fd5"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "5"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "\n",
-    "array_1d [-1]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "JROW8R8dNxPb",
-    "outputId": "ad5890d9-a8a6-445b-b5bd-c4a468ddde62"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([3, 4])"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# Slicing: Returning the grou of element from an array\n",
-    "\n",
-    "array_1d [2:4]"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "XCR7_WPnUM2M"
-   },
-   "source": [
-    "### 2.2 2D Array Indexing and Selection"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {
-    "id": "0q6e67_2O60m"
-   },
-   "outputs": [],
-   "source": [
-    "## Indexing 2D array\n",
-    "\n",
-    "array_2d = np.array([[1,2,3],[4,5,6],[7,8,9]])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "5v3HKOHoQP2t",
-    "outputId": "628fe748-a55c-400c-bf31-5a62848574d5"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "5"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Selecting individual element\n",
-    "## array_2d[row][column]\n",
-    "## let's select 5..that is row 1, column 1 (we start from 0!!)\n",
-    "\n",
-    "array_2d[1][1]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "cZhbAnqNR6jQ",
-    "outputId": "78b52c43-6dd0-4254-9e20-51bec4bf5c3c"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "9"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# let's select 9..that is row 2, column 2\n",
-    "\n",
-    "array_2d[2][2]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "B0GnGJCOSDka",
-    "outputId": "31e447b6-3a57-453b-bfc2-bd6050f07632"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([4, 5, 6])"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Selecting whole row\n",
-    "#array_2d[row]\n",
-    "\n",
-    "array_2d[1]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "8OHO4oTHSROF",
-    "outputId": "ee50a860-3233-4fb3-bfa1-a71f2f70ea2e"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3],\n",
-       "       [4, 5, 6]])"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Selecting group of elements in 2D array\n",
-    "## array_2d[rows, columns]..You select rows and columns\n",
-    "\n",
-    "## Let's select the first two rows\n",
-    "## Rows :2 denotes that we are selecting all rows up to the second. \n",
-    "## Columns : denotes that all columns are selected.\n",
-    "\n",
-    "\n",
-    "array_2d[:2,:]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "NIkqcMKr0xoJ",
-    "outputId": "f7895d25-a1ed-4eae-d2d1-624e03541d2b"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2],\n",
-       "       [4, 5]])"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "\n",
-    "## Selecting all first two rows and first two columns\n",
-    "\n",
-    "array_2d[:2,0:2]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "HPwIW3HSTPPu",
-    "outputId": "a3cfa1ba-237b-4201-e6f6-7616b8b4b8da"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3],\n",
-       "       [4, 5, 6]])"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Above is same as\n",
-    "\n",
-    "array_2d[0:2,:]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "hLC6LNsLTdNL",
-    "outputId": "61247100-b491-4a59-95a3-d2d344d83ea7"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3],\n",
-       "       [4, 5, 6],\n",
-       "       [7, 8, 9]])"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## This will return all rows, and so all columns and so same as orginal array\n",
-    "array_2d[0:3,:]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "FNV1X16NUbpJ",
-    "outputId": "7f42ed6b-2ed0-406d-dd47-1907202f0b01"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([7, 8, 9])"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## return the second row\n",
-    "\n",
-    "array_2d[2,:]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "XndtDh1NUmpp",
-    "outputId": "42db9c63-a4c5-47d0-8d9d-b6d7d87b61c3"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([3, 6, 9])"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## return the second column\n",
-    "\n",
-    "array_2d[:,2]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "N9YTUJNjUxdd",
-    "outputId": "08078a90-9fe5-45f6-d618-5ba3a2ea7271"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[2, 3],\n",
-       "       [5, 6],\n",
-       "       [8, 9]])"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## return the last two columns\n",
-    "\n",
-    "array_2d[:,1:3]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "eOcqJEbxU6iR",
-    "outputId": "a0fd909a-5704-42f7-b841-663a943d3f89"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 4, 7])"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## return the first column\n",
-    "\n",
-    "array_2d[:,0]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "OeKEcYRCVKdJ",
-    "outputId": "5b10b5a5-fdf5-47c0-bd2b-d577c51ed1ad"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 2, 3])"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## return the first row\n",
-    "\n",
-    "array_2d[0,:]"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "mgnarYNHVXUT"
-   },
-   "source": [
-    "Indexing or selecting 2D array may seems confusing but when you try it multiple times, you get the idea. If you are selecting an entire row, that means the all the columns are selected (but not their all values). And vice versa. \n",
-    "\n",
-    "As shown below, we are selecting the first row, but as you can see all columns are selected (:).\n",
-    "\n",
-    "```\n",
-    "array_2d[0,:]\n",
-    "```\n",
-    "\n",
-    "\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "zc1Iyb91WHxf"
-   },
-   "source": [
-    "### 2.3 Conditional selection\n",
-    "\n",
-    "You can use a condition to select values in an array. Let's use comparison operators to select the values. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {
-    "id": "ANqjpFENWKCM"
-   },
-   "outputs": [],
-   "source": [
-    "## Let's create an array\n",
-    "\n",
-    "arr= np.array(([1,2,3],[4,5,6],[7,8,9]))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Y9qhO4QaZksn",
-    "outputId": "d31bfcf8-06b8-4b8d-d4da-c6478cd1d58a"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 2, 3, 4, 5])"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Select all elements in an array which are less than 6\n",
-    "\n",
-    "arr[arr <6 ]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "GNY9S75DZusJ",
-    "outputId": "0642da71-f959-4063-8984-83b55e2bd909"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([7, 8, 9])"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Select all elements in an array which are greater than 6\n",
-    "\n",
-    "arr[arr > 6]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "REbbdFOBaBc6",
-    "outputId": "141149de-62ab-4427-ae0a-198117ebda1a"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([2, 4, 6, 8])"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Select all even numbers in an array\n",
-    "\n",
-    "arr[arr % 2 ==0 ]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "ZXeWnQ6maY8A",
-    "outputId": "e8e92e29-2fe7-4c48-9bc5-0bab5cab8a57"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 3, 5, 7, 9])"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Select all odd numbers in an array\n",
-    "\n",
-    "arr[arr % 2 !=0 ]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "TQKfIyGzaeAD",
-    "outputId": "72fa895b-2367-4c56-b3fc-76d07a834d17"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([5, 7, 9])"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## You can also have multiple conditions\n",
-    "\n",
-    "## In all odd numbers, return values which are greater or equal to 5\n",
-    "\n",
-    "\n",
-    "arr[(arr % 2 !=0 ) & (arr >=5) ]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "LvQZsD8UbL2I",
-    "outputId": "dbe32118-6aa3-4b43-ee37-16eff39839e1"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[False, False, False],\n",
-       "       [False, False,  True],\n",
-       "       [ True,  True,  True]])"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Using logical selection, you can also return True for values in which a given condition is met in an array\n",
-    "\n",
-    "arr > 5"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "HGCXwMc-byoh",
-    "outputId": "a8003057-2167-4c15-c240-4c56dcbe3e74"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[False, False, False],\n",
-       "       [False, False, False],\n",
-       "       [False, False, False]])"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## We do not have 0 in our array\n",
-    "\n",
-    "arr == 0"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "kKTlmkV1cM1F"
-   },
-   "source": [
-    "<a name='3'></a>\n",
-    "## 3. Basic Array Operations\n",
-    "\n",
-    "### 3.1 Quick Arithmetic operation: Addition, Subtraction, Multiplication, Division, Squaring"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {
-    "id": "kVyV9yZEcphH"
-   },
-   "outputs": [],
-   "source": [
-    "# Let's create two arrays\n",
-    "\n",
-    "arr1 = np.arange(0,5)\n",
-    "arr2 = np.arange(6,11)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "k-XbCI7DdGSC",
-    "outputId": "b0e463c1-3906-41c7-f98d-ec53596eadc1"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 6,  8, 10, 12, 14])"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Addition\n",
-    "\n",
-    "arr1 + arr2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "HRO_en3BeOEr",
-    "outputId": "afba0120-901e-4c4e-8add-87aa4c326f34"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([6, 6, 6, 6, 6])"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Subtraction\n",
-    "\n",
-    "arr2 - arr1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "nQB3wfgneak3",
-    "outputId": "b1e9b19f-44f5-4298-e478-ff4f07c2a231"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0,  7, 16, 27, 40])"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Multiplication\n",
-    "\n",
-    "arr1 * arr2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "-N1pyoXjej_Y",
-    "outputId": "4ca31127-9cf6-4147-d165-8f51647a3fa0"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0.        , 0.14285714, 0.25      , 0.33333333, 0.4       ])"
-      ]
-     },
-     "execution_count": 53,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Division\n",
-    "\n",
-    "arr1 / arr2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "De6gp_lvetPf",
-    "outputId": "aa0b12f5-ad61-4e88-e2ac-50d79ade09e1"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0,  1,  4,  9, 16])"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Squaring\n",
-    "\n",
-    "arr1 ** 2"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "Ual-ST0-fhCZ"
-   },
-   "source": [
-    "### 3.2 Universal functions\n",
-    "\n",
-    "NumPy universal functions (`ufunc`) allows to compute math, trigonometric, logical and comparison operations such as sin, cos, tan, exponent(exp), log, square, greater, less, etc..."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {
-    "id": "aJfRCWLcfwTr"
-   },
-   "outputs": [],
-   "source": [
-    "## creating two arrays \n",
-    "\n",
-    "arr1 = np.arange(0,5)\n",
-    "arr2 = np.arange(6,11)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "a3QsqIJ4NNxf",
-    "outputId": "094569fa-3458-4022-f4e2-a31aaca28f8e"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 6,  8, 10, 12, 14])"
-      ]
-     },
-     "execution_count": 56,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the sum of two arrays\n",
-    "\n",
-    "np.add(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "43f5eAagNb3J",
-    "outputId": "e9c826cb-26ff-437d-cfe3-191c43fb49f9"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0,  7, 16, 27, 40])"
-      ]
-     },
-     "execution_count": 57,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the product of two arrays\n",
-    "\n",
-    "np.multiply(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "NBG0EPBuNiDZ",
-    "outputId": "3063e564-8824-41cb-f07d-af0b83c1fe0f"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([-6, -6, -6, -6, -6])"
-      ]
-     },
-     "execution_count": 58,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the difference between two arrays\n",
-    "\n",
-    "np.subtract(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "XpgZ6O50NwYa",
-    "outputId": "5578dc8b-be68-4172-ca25-b34fd96afbb1"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0.        , 0.14285714, 0.25      , 0.33333333, 0.4       ])"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the division of two arrays\n",
-    "\n",
-    "np.divide(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "K3Bc6goeHIch",
-    "outputId": "63ea938d-3a71-4066-fc7a-26f8a60ed205"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0.        ,  0.84147098,  0.90929743,  0.14112001, -0.7568025 ])"
-      ]
-     },
-     "execution_count": 60,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the sin of arr1\n",
-    "\n",
-    "np.sin(arr1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Zj05py4IIugZ",
-    "outputId": "6b4eb73e-7d44-4650-81a7-80b5c856d4b1"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0.        ,  0.85090352,  0.89399666, -0.80115264])"
-      ]
-     },
-     "execution_count": 61,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.sin([0,45,90,180])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "fDo3b-qRIYHR",
-    "outputId": "52ad4b89-32ad-4b80-e430-fc5b337fb25e"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 1.        ,  0.54030231, -0.41614684, -0.9899925 , -0.65364362])"
-      ]
-     },
-     "execution_count": 62,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the cosine of arr 1\n",
-    "\n",
-    "np.cos(arr1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "FsirUyFCIit9",
-    "outputId": "402832da-0a17-4a08-d79d-007ab61a8014"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 1.        ,  0.52532199, -0.44807362, -0.59846007])"
-      ]
-     },
-     "execution_count": 63,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.cos([0,45,90,180])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "XQR8m4HxI1E8",
-    "outputId": "d6434e9b-5527-4466-ac58-6455b3aa15ed"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([-0.29100619,  0.87144798, -6.79971146, -0.45231566,  0.64836083])"
-      ]
-     },
-     "execution_count": 64,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the tangent(tan) of the array\n",
-    "\n",
-    "np.tan(arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "PIOUpa_gJFuv",
-    "outputId": "081b23b0-c74d-4862-b27b-d91cbbffb002"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1.79175947, 1.94591015, 2.07944154, 2.19722458, 2.30258509])"
-      ]
-     },
-     "execution_count": 65,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the logarithmic(log) of the array\n",
-    "\n",
-    "np.log(arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 66,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "b_QsfHLDJVyq",
-    "outputId": "5c73fd2b-3c9a-4921-ab7c-e40b8d20b8c6"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([  403.42879349,  1096.63315843,  2980.95798704,  8103.08392758,\n",
-       "       22026.46579481])"
-      ]
-     },
-     "execution_count": 66,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the exponent(exp or e^) of the array\n",
-    "\n",
-    "np.exp(arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 67,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "s2wDCGMfJfE-",
-    "outputId": "4ed21980-3170-4c47-e1b8-4d268af93560"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([      0,       1,     256,   19683, 1048576])"
-      ]
-     },
-     "execution_count": 67,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the power  of the array\n",
-    "## Array 1 is powered array 2...0^6=0, 1^7=1, 2^8=256, etc..\n",
-    "\n",
-    "np.power(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 68,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "bYGyzm0lKh0b",
-    "outputId": "240eb78c-74db-45e8-f2e2-a314d1e54e2d"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([False, False, False, False, False])"
-      ]
-     },
-     "execution_count": 68,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Comparison operations return true or false\n",
-    "## Arr 1 is less than arr 2...so that's false\n",
-    "\n",
-    "np.greater(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 69,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "rXJJKyJhLfy4",
-    "outputId": "cb9c2426-1068-464c-bae3-f57bf2f5614d"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ True,  True,  True,  True,  True])"
-      ]
-     },
-     "execution_count": 69,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Comparison operations return true or false\n",
-    "## Arr 1 is less than arr 2...so that's true\n",
-    "\n",
-    "np.less(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "6a6Agz1yOAvn"
-   },
-   "source": [
-    "<a name='4'></a>\n",
-    "## 4. Basic Statistics\n",
-    "\n",
-    "With NumPy, we can compute the basic statistics such as the standard deviation (std), variance (var),mean, median, minimum value, maximum value of an array. \n",
-    "\n",
-    "More about NumPy statistics: https://numpy.org/doc/stable/reference/routines.statistics.html#order-statistics"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 70,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "7ZQedUDGHW60",
-    "outputId": "9828d039-3399-4ac4-ff6a-00b5a9b461d4"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4])"
-      ]
-     },
-     "execution_count": 70,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Creating an array \n",
-    "\n",
-    "arr = np.arange(0,5)\n",
-    "arr"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "8eXcY0qjKWtx"
-   },
-   "source": [
-    "### 4.1 Standard Deviation"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 71,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "t-s8L0VJQtpA",
-    "outputId": "716cfeeb-d69b-47e4-cf28-f58fadf1c97b"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1.4142135623730951"
-      ]
-     },
-     "execution_count": 71,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## calculating the standard deviation of the array\n",
-    "## Std is how much an element of the array deviates from the mean of the array\n",
-    "\n",
-    "np.std(arr)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 72,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "PhWndlxuHnrK",
-    "outputId": "608573b6-e1a4-49f6-864b-bfdbc123e578"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1.118033988749895"
-      ]
-     },
-     "execution_count": 72,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr2 = np.array([[3,4], [5,6]])\n",
-    "\n",
-    "np.std(arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 73,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "IH2BFcuZH_jc",
-    "outputId": "530fd53e-1acd-4a70-f401-6f9455641b32"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1., 1.])"
-      ]
-     },
-     "execution_count": 73,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Specifying the axis\n",
-    "## By default, the std is computed on the flattened values (or converted into a single column vector)\n",
-    "\n",
-    "np.std(arr2, axis=0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 74,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "fSCEMvzNIdpZ",
-    "outputId": "691b6163-8eed-4dfc-ae99-72fe0541fea6"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0.5, 0.5])"
-      ]
-     },
-     "execution_count": 74,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.std(arr2, axis=1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "HK8EvjAcKecA"
-   },
-   "source": [
-    "### 4.2 Variance"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 75,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "3DavtYCiIjDY",
-    "outputId": "9735e45c-c03b-40c6-888b-e9da82cd2b55"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2.0"
-      ]
-     },
-     "execution_count": 75,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the Variance (var)\n",
-    "\n",
-    "arr = np.arange(0,5)\n",
-    "\n",
-    "np.var(arr)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 76,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Av4TeSiBI0c9",
-    "outputId": "985ebbf3-f3bc-4604-fae6-e5fee28ec26c"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1.25"
-      ]
-     },
-     "execution_count": 76,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.var(arr2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "B_n2hLsiKq7e"
-   },
-   "source": [
-    "### 4.3 Mean"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 77,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "O1rlEIMiI5aO",
-    "outputId": "a20c288f-9003-43b3-e240-ad33cda96223"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2.0"
-      ]
-     },
-     "execution_count": 77,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the mean of the array\n",
-    "\n",
-    "np.mean(arr)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 78,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "evY84_vLJqe_",
-    "outputId": "1d3571d4-3f8f-477e-bb12-61e2282995d3"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2.0"
-      ]
-     },
-     "execution_count": 78,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## mean gives the same results as the average\n",
-    "np.average(arr)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "xmHcYNRWK0tX"
-   },
-   "source": [
-    "### 4.4 Median"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 79,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "O3ZIMTETJIyk",
-    "outputId": "96fd4a52-04c4-495d-ecf7-f173bc160e1a"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2.0"
-      ]
-     },
-     "execution_count": 79,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the median of the array\n",
-    "\n",
-    "np.median(arr)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "_AkHlz-RK5jP"
-   },
-   "source": [
-    "### 4.3 Minimum and Maximum"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 80,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "XIoaY7s_JoQB",
-    "outputId": "acc350e5-7876-40b2-b5f9-24da2add27ac"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0"
-      ]
-     },
-     "execution_count": 80,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the minimum value\n",
-    "\n",
-    "np.min(arr)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 81,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "mgjxq1w1KAiH",
-    "outputId": "ed372591-6272-43f6-a03b-543785ce58ca"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "4"
-      ]
-     },
-     "execution_count": 81,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the maximum value\n",
-    "\n",
-    "np.max(arr)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "pZ3JuNw7MwaS"
-   },
-   "source": [
-    "<a name='5'></a>\n",
-    "## 5. Data Manipulation\n",
-    "\n",
-    "Data Manipulation is important step in Machine Learning project. Let's some of NumPy methods and functions which are useful in data manipulation. "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "0TalsnPCkq1X"
-   },
-   "source": [
-    "### 5.1 Shape of the array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 82,
-   "metadata": {
-    "id": "YG_YOgh5kwdL"
-   },
-   "outputs": [],
-   "source": [
-    "## Creating an array \n",
-    "\n",
-    "arr1 = np.arange(0,10)\n",
-    "arr2 = np.array(([1,2,3],[4,5,6],[7,8,9]))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 83,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "cubkv1UCnEbW",
-    "outputId": "f8733420-89e4-4147-f7f9-6525290d9851"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
-      ]
-     },
-     "execution_count": 83,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 84,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "7Q3PRJN3nIZ3",
-    "outputId": "f292d52b-2e0e-4205-d27f-d95570a5e852"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3],\n",
-       "       [4, 5, 6],\n",
-       "       [7, 8, 9]])"
-      ]
-     },
-     "execution_count": 84,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 85,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "YBLLedf7kzJI",
-    "outputId": "3a10664b-70ac-423c-f005-8929979ae309"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(10,)"
-      ]
-     },
-     "execution_count": 85,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.shape(arr1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 86,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "0LoJBrQSk9vk",
-    "outputId": "b15f5438-702b-4cc7-bd9a-0b4665516e31"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(3, 3)"
-      ]
-     },
-     "execution_count": 86,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.shape(arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 87,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "C5vsZtE1lSM2",
-    "outputId": "4cebb28f-dbfa-43c1-83ec-ef07a2580a5e"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(3, 3)"
-      ]
-     },
-     "execution_count": 87,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr2.shape"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "lbjzG0Xrlcbl"
-   },
-   "source": [
-    "### 5.2 Shaping the Array\n",
-    "\n",
-    "`np.reshape(array_name, newshape=(rows, columns)` or `array_name.reshape(rows, columns)` change the shape of the array. The rows and columns of the new shape has to comform with the existing data of the array. Otherwise, it won't work. Take an example, you can convert (3,3) array into (1,9) but you can't convert it into (5,5). "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 88,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "GkU2npH-le_9",
-    "outputId": "a4ac26c0-db89-4b11-e1c9-46dc5a71785f"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[0, 1],\n",
-       "       [2, 3],\n",
-       "       [4, 5],\n",
-       "       [6, 7],\n",
-       "       [8, 9]])"
-      ]
-     },
-     "execution_count": 88,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### arr1 is (10,)....10 rows, 1 column. Let's reshape it into (5,2)\n",
-    "np.reshape(arr1, newshape=(5,2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 89,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "52ls1fjDl9m3",
-    "outputId": "4bdca11e-b2af-4924-de31-24f29863f375"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[0, 1],\n",
-       "       [2, 3],\n",
-       "       [4, 5],\n",
-       "       [6, 7],\n",
-       "       [8, 9]])"
-      ]
-     },
-     "execution_count": 89,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## This would also work\n",
-    "arr1.reshape(5,2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 90,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Mh8_zejvmnRs",
-    "outputId": "f720d0f5-1a55-41ed-c9ca-8d094f8405a2"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3, 4, 5, 6, 7, 8, 9]])"
-      ]
-     },
-     "execution_count": 90,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr2_reshaped = arr2.reshape(9,1)\n",
-    "arr2_reshaped.T"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 91,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "gD1_rWyumsxX",
-    "outputId": "97d95a9f-c806-46e5-86c2-dd660d7465f3"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3],\n",
-       "       [4, 5, 6],\n",
-       "       [7, 8, 9]])"
-      ]
-     },
-     "execution_count": 91,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr2_reshaped.reshape(3,3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 92,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Iyfh1tWr2VTe",
-    "outputId": "fcbac3c5-86b0-41fd-c37a-eb350e22ce6b"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3, 4, 5, 6, 7, 8, 9]])"
-      ]
-     },
-     "execution_count": 92,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## np.resize can also be used to change the shape of the array into a specific size\n",
-    "\n",
-    "np.resize(arr2, (1,9))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "jPF2gp6PoZK-"
-   },
-   "source": [
-    "### 5.3 Copying array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 93,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "MGacJLaVoZq7",
-    "outputId": "298de278-da88-4f7c-f891-64e37e3b81ea"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
-      ]
-     },
-     "execution_count": 93,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr1 = np.arange(0,10)\n",
-    "arr1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 94,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "ahDMt-anohhh",
-    "outputId": "c65d2739-0914-41b9-9b0c-15e3ae86f2d3"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
-      ]
-     },
-     "execution_count": 94,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr1_copy = arr1.copy()\n",
-    "arr1_copy"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 95,
-   "metadata": {
-    "id": "WQy97R5Wo375"
-   },
-   "outputs": [],
-   "source": [
-    "## Copying the values of one array into the other \n",
-    "\n",
-    "## Let's copy array 2 into 1 --they have the same shape\n",
-    "\n",
-    "arr1 = np.arange(0,6)\n",
-    "arr2 = np.arange(6,12)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 96,
-   "metadata": {
-    "id": "DdE9pVVdppQ8"
-   },
-   "outputs": [],
-   "source": [
-    "## arr1 is destination, arr2 is source\n",
-    "np.copyto(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 97,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "GhzDAFp2qFgu",
-    "outputId": "801466ef-27ec-4e4d-9678-7b5793356227"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 6,  7,  8,  9, 10, 11])"
-      ]
-     },
-     "execution_count": 97,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr1"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "EScZw0b9rDV-"
-   },
-   "source": [
-    "### 5.4 Joining arrays"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 98,
-   "metadata": {
-    "id": "yVm7cXphrLQD"
-   },
-   "outputs": [],
-   "source": [
-    "### Creating two arrays\n",
-    "\n",
-    "arr1 = np.array([[1,2,3],[4,5,6],[7,8,9]])\n",
-    "arr2 = np.array([[10,11,12]])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 99,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "h5TXwNZErU6g",
-    "outputId": "49113d3c-87dc-4643-8f43-d0be74c5460d"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[ 1,  2,  3],\n",
-       "       [ 4,  5,  6],\n",
-       "       [ 7,  8,  9],\n",
-       "       [10, 11, 12]])"
-      ]
-     },
-     "execution_count": 99,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Joining them\n",
-    "\n",
-    "np.concatenate((arr1, arr2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 100,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "f36TbVcsrVRg",
-    "outputId": "4e785c77-4203-4bee-fe05-cddd8654147c"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[ 1,  2,  3, 10],\n",
-       "       [ 4,  5,  6, 11],\n",
-       "       [ 7,  8,  9, 12]])"
-      ]
-     },
-     "execution_count": 100,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Transposing arr2\n",
-    "## arr2.T is transpose operation\n",
-    "\n",
-    "np.concatenate((arr1, arr2.T), axis=1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 101,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "4XrLudetsvl0",
-    "outputId": "93f316b1-0fa9-4696-9455-395ddc16662b"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12])"
-      ]
-     },
-     "execution_count": 101,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### Setting axis to none flatten the array\n",
-    "\n",
-    "np.concatenate((arr1, arr2), axis=None)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 102,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "bVQMnJais7_6",
-    "outputId": "ab2f34c0-6e2a-49b9-b6fe-1ff22d264289"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[ 0,  6],\n",
-       "       [ 1,  7],\n",
-       "       [ 2,  8],\n",
-       "       [ 3,  9],\n",
-       "       [ 4, 10],\n",
-       "       [ 5, 11]])"
-      ]
-     },
-     "execution_count": 102,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### Joining two 1Ds array into 2D array: Stacking\n",
-    "\n",
-    "# Column stacking\n",
-    "\n",
-    "arr1 = np.arange(0,6)\n",
-    "arr2 = np.arange(6,12)\n",
-    "\n",
-    "np.column_stack((arr1, arr2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 103,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "utJCDp08toet",
-    "outputId": "aad307f9-3caf-448d-cd28-4cc062ef8cc5"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[ 0,  1,  2,  3,  4,  5],\n",
-       "       [ 6,  7,  8,  9, 10, 11]])"
-      ]
-     },
-     "execution_count": 103,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Row stacking \n",
-    "\n",
-    "np.row_stack((arr1, arr2))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "pSk67COOuFJw"
-   },
-   "source": [
-    "### 5.5 Splitting arrays"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 104,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "uPQ3pHuyuJrb",
-    "outputId": "1056b6ad-49ee-4234-cc10-0a7cc2a640b2"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4, 5])"
-      ]
-     },
-     "execution_count": 104,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr1 = np.arange(0,6)\n",
-    "arr1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 105,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "axVESXYzufxz",
-    "outputId": "a3ae64d1-2374-44e2-d99e-ba6113a36b5e"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[array([0, 1, 2]), array([3, 4, 5])]"
-      ]
-     },
-     "execution_count": 105,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### Splitting the array into two arrays\n",
-    "\n",
-    "np.split(arr1, 2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 106,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "NYw7-G0Ovs9u",
-    "outputId": "a15d5f79-a209-401b-9a7d-74e6216acbde"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[array([0, 1]), array([2, 3]), array([4, 5])]"
-      ]
-     },
-     "execution_count": 106,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### Splitting the array into three arrays\n",
-    "\n",
-    "np.split(arr1, 3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "rwOOipKsxEBl"
-   },
-   "source": [
-    "### 5.6 Adding and repeating elements in an array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 107,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "tnDE_kxxxPZI",
-    "outputId": "71daa4f8-fef7-46ba-ea2c-3d6c0d32af58"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4, 5])"
-      ]
-     },
-     "execution_count": 107,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr1 = np.arange(0,6)\n",
-    "arr1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 108,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "qiWApvvXxSyq",
-    "outputId": "e2f29e19-340a-4d2c-b165-1d30d4c5831b"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4, 5, 7])"
-      ]
-     },
-     "execution_count": 108,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Adding the values at the end of the array\n",
-    "np.append(arr1,7)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 109,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "mzA7NlQKzPN4",
-    "outputId": "e9216924-9372-4b9e-c0e0-3fd174673214"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3, 1, 2, 3, 1, 2, 3]])"
-      ]
-     },
-     "execution_count": 109,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### Given an array, can you add itself multiple times? or repeat it?\n",
-    "\n",
-    "arr = np.array([[1,2,3]])\n",
-    "np.tile(arr, 3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 110,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "XCkeeaBl0lT4",
-    "outputId": "202b85dd-3f21-408b-ce03-8c9767f116e3"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 1, 1, 2, 2, 2, 3, 3, 3])"
-      ]
-     },
-     "execution_count": 110,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.repeat(arr,3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "3mg3ZMav4HIb"
-   },
-   "source": [
-    "### 5.7 Sorting elements in an array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 111,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "02qT1kUs4L01",
-    "outputId": "5929d293-4a14-4ff8-f543-27ef512c2da7"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 7, 7, 9]])"
-      ]
-     },
-     "execution_count": 111,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr = np.array([[1,2,3,4,5,3,2,1,3,5,6,7,7,5,9,5]])\n",
-    "\n",
-    "np.sort(arr)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 112,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "z_b7H94nx61s",
-    "outputId": "dcadd4d3-695c-4a71-c305-f93dda910bb3"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 2, 3, 4, 5, 6, 7, 9])"
-      ]
-     },
-     "execution_count": 112,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Finding the unique elements in an array\n",
-    "\n",
-    "arr = np.array([[1,2,3,4,5,3,2,1,3,5,6,7,7,5,9,5]])\n",
-    "\n",
-    "np.unique(arr)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "assBn6MPAOaW"
-   },
-   "source": [
-    "### 5.8 Reversing an array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 113,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "E1aycT_l1Acu",
-    "outputId": "e9145b3f-7f68-4d95-8d81-34f959c17fbb"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3],\n",
-       "       [4, 5, 6],\n",
-       "       [7, 8, 9]])"
-      ]
-     },
-     "execution_count": 113,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## You can also flip the array\n",
-    "\n",
-    "arr = np.array([[1,2,3],[4,5,6],[7,8,9]])\n",
-    "arr"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 114,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "5DwhyTxY17Wx",
-    "outputId": "d255183a-eb16-4117-ea35-31439a19840b"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[7, 8, 9],\n",
-       "       [4, 5, 6],\n",
-       "       [1, 2, 3]])"
-      ]
-     },
-     "execution_count": 114,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Up/down flipping\n",
-    "\n",
-    "np.flipud(arr)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 115,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "XQTBiI5m19gh",
-    "outputId": "215de3e1-9884-44be-c7b2-93e09803ee15"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[3, 2, 1],\n",
-       "       [6, 5, 4],\n",
-       "       [9, 8, 7]])"
-      ]
-     },
-     "execution_count": 115,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## left/right flipping\n",
-    "\n",
-    "np.fliplr(arr)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "mBh5uGjL4ZBq"
-   },
-   "source": [
-    "\n",
-    "\n",
-    "---\n",
-    "\n",
-    "\n",
-    "\n",
-    "---\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "dIRTQbdH2wzC"
-   },
-   "source": [
-    "That's it for NumPy. In this lab, you learned how to create an array, perform basic operations, and also how to manipulate an array. \n",
-    "\n",
-    "It's kind of fascinating to think how tools like `TensorFlow, Sklearn, Pandas....` are powered by NumPy. \n",
-    "\n",
-    "In the next lab, we will learn about the Pandas, another important tool used for real world data manipulation."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### [BACK TO TOP](#0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "colab": {
-   "name": "1. Intro to NumPy for Data Computation.ipynb",
-   "provenance": []
-  },
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.7.10"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
diff --git a/1_data_computations_with_numpy/.ipynb_checkpoints/1_Intro to NumPy for Data Computation-checkpoint.ipynb b/1_data_computations_with_numpy/.ipynb_checkpoints/1_Intro to NumPy for Data Computation-checkpoint.ipynb
deleted file mode 100644
index 2d2e6fc..0000000
--- a/1_data_computations_with_numpy/.ipynb_checkpoints/1_Intro to NumPy for Data Computation-checkpoint.ipynb	
+++ /dev/null
@@ -1,3487 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "Od0BVxJyFiMZ"
-   },
-   "source": [
-    " # Intro to NumPy for Data Computations\n",
-    "\n",
-    "This is lab is performing data computations with NumPy. NumPy is a scientific tool used to make mathematical computations easily. \n",
-    "\n",
-    "In this lab, you will learn to:\n",
-    "\n",
-    " * [1. Create a NumPy array](#1)\n",
-    " * [2. Select data: indexing and slicing of array](#2)\n",
-    " * [3. Perform mathematical and other basic operations](#3)\n",
-    " * [4. Perform basic statistics](#4)\n",
-    " * [5. Manipulate data](#5)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "2MG9Fii1d8Wy"
-   },
-   "source": [
-    "If you are using Google Colab, we do not need to install NumPy. We will only have to import it just like this:\n",
-    "\n",
-    "`import numpy as np`\n",
-    "\n",
-    "If you are using local Jupyter notebooks, make sure you have it installed already."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "XzRyETjqGuLE"
-   },
-   "source": [
-    "<a name='1'></a>\n",
-    "## 1. Creating an Array in NumPy\n",
-    "\n",
-    "Array can either be vector or matrice. A vector is one dimensional array, and a matrix is a two or more dimensional array. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {
-    "id": "rFx8BN4bfTWL"
-   },
-   "outputs": [],
-   "source": [
-    "## Importing numpy\n",
-    "\n",
-    "import numpy as np"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "tO9qq2UEGx6M",
-    "outputId": "490647a5-f8fb-4459-eeba-d3657d998afa"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 2, 3, 4, 5])"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Creating a simple 1 dimensional array: vector\n",
-    "np.array([1,2,3,4,5])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "o27WSEaWetl6",
-    "outputId": "3b3406cf-31f1-483f-c0f8-0715dabf5e01"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[ 1,  2,  3,  4,  5],\n",
-       "       [ 6,  7,  8,  9, 10]])"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Creating 2 dimensional array: matrix\n",
-    "\n",
-    "np.array([(1,2,3,4,5), (6,7,8,9,10)])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "m9sI1bT0fjMK",
-    "outputId": "c521c0c5-aba9-40da-aa51-ccd51e11a967"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 2, 3, 4, 5])"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Creating an array from a list\n",
-    "\n",
-    "num_list = [1,2,3,4,5]\n",
-    "\n",
-    "np.array(num_list)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Jo2YqycbgiHV",
-    "outputId": "fb8b61f7-5a05-46d3-e688-ea82991deb2d"
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[1 2 3 4 5]\n"
-     ]
-    }
-   ],
-   "source": [
-    "print(np.array(num_list))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "FWI8bsvmgXfs"
-   },
-   "source": [
-    "### 1.1 Generating Array\n",
-    "\n",
-    "NumPy offers various options to generate an array depending on particular need, such as:\n",
-    "\n",
-    "* Generating identity array\n",
-    "* Generating zero array of a given size\n",
-    "* Generating ones array with a given size\n",
-    "* Generating an array in a given range\n",
-    "* Generating an array with random values\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "OTjgeBrzaDQl",
-    "outputId": "2a2fd24e-5faf-4d51-c450-0249377a9842"
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[1. 0. 0. 0.]\n",
-      " [0. 1. 0. 0.]\n",
-      " [0. 0. 1. 0.]\n",
-      " [0. 0. 0. 1.]]\n"
-     ]
-    }
-   ],
-   "source": [
-    "## Generating an identity array \n",
-    "\n",
-    "identity_array = np.identity(4)\n",
-    "print(identity_array)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "yIt4o9lBgZqo",
-    "outputId": "6632591d-0203-433c-ba07-2376d8b25790"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1., 0., 0., 0.],\n",
-       "       [0., 1., 0., 0.],\n",
-       "       [0., 0., 1., 0.],\n",
-       "       [0., 0., 0., 1.]])"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Generating an identity matrix of 1s\n",
-    "\n",
-    "np.eye(4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Bo3PEZahhnGl",
-    "outputId": "903bfb68-772e-473f-9c7b-9c8461a1a7bf"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[7., 0., 0., 0.],\n",
-       "       [0., 7., 0., 0.],\n",
-       "       [0., 0., 7., 0.],\n",
-       "       [0., 0., 0., 7.]])"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# You can multiply with any constant\n",
-    "\n",
-    "np.eye(4) * 7"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "4yZIO0FWhzv7",
-    "outputId": "15ad3530-0084-4c15-a356-42addb755332"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0., 0., 0., 0., 0.])"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# Generating zero array of a given size\n",
-    "# 1 dimensional zero array\n",
-    "np.zeros(5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Ys3edWPOigeX",
-    "outputId": "4017496b-ffd9-443a-fa1c-ae167ff817ac"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[0., 0., 0., 0., 0., 0.],\n",
-       "       [0., 0., 0., 0., 0., 0.],\n",
-       "       [0., 0., 0., 0., 0., 0.],\n",
-       "       [0., 0., 0., 0., 0., 0.],\n",
-       "       [0., 0., 0., 0., 0., 0.]])"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# Creating two dimensional array: pass the tuple of rows and columns' number\n",
-    "#np.zeros((rows, columns))\n",
-    "\n",
-    "np.zeros((5,6))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "l5hEgxuYiphg",
-    "outputId": "f35fae1f-9cf3-44ee-bff2-9444e4aa28ae"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1., 1., 1., 1., 1.])"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# Generating ones array of a given size\n",
-    "# 1 dimensional one array\n",
-    "\n",
-    "np.ones(5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "S9Tb6tjgjNIW",
-    "outputId": "8216c53d-f9e6-48f7-b106-2f7a71851ac0"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1., 1., 1., 1., 1., 1.],\n",
-       "       [1., 1., 1., 1., 1., 1.],\n",
-       "       [1., 1., 1., 1., 1., 1.],\n",
-       "       [1., 1., 1., 1., 1., 1.],\n",
-       "       [1., 1., 1., 1., 1., 1.]])"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# Creating two dimensional ones array: pass the tuple of rows and columns' number\n",
-    "# np.ones((rows, columns))\n",
-    "\n",
-    "np.ones((5,6))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "iB2v6pfLjWIG",
-    "outputId": "dfe3950c-8b34-48c1-8af9-27dbc48a3af3"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4])"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Generating an array in a given range or interval\n",
-    "\n",
-    "np.arange(0,5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "IldBA00wjrMc",
-    "outputId": "68416c4e-5f56-4a48-df21-b62a767088b9"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0,  2,  4,  6,  8, 10, 12, 14, 16, 18])"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## If you want to control the step size\n",
-    "\n",
-    "np.arange(0,20,2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "kXJAdbO3j1Fv",
-    "outputId": "f278ab62-d48e-4fda-b834-ca7570047ab5"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0.,  5., 10., 15., 20.])"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## You can also use linspace to generate an evenly spaced numbers in a given interval\n",
-    "\n",
-    "np.linspace(0,20,5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "m7wEgM3LkMD7",
-    "outputId": "1b3fb3cd-c3d6-4596-e4c6-c91f21de6f73"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([  0.,  25.,  50.,  75., 100.])"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "\n",
-    "np.linspace(0,100,5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Gk1TCkP_kRKM",
-    "outputId": "1e1075c2-47dc-4abd-a784-5d9fb88f7802"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0.        ,  1.11111111,  2.22222222,  3.33333333,  4.44444444,\n",
-       "        5.55555556,  6.66666667,  7.77777778,  8.88888889, 10.        ])"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.linspace(0,10,10)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "422VmvKLkUIm",
-    "outputId": "3805deac-07ae-4d18-b478-e44ba12305d8"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0.68944519, 0.25872307, 0.7565542 , 0.68606423])"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Generating an array with random values\n",
-    "# Create a 1D array with 4 random numbers\n",
-    "\n",
-    "np.random.rand(4)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "_In_Ydv-kt_j",
-    "outputId": "735b1c2e-da13-414e-d773-a56d20745ef7"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0.41979127, 0.83292096, 0.50330078, 0.17331376])"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.random.rand(4)\n",
-    "\n",
-    "#We will not get teh same values"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "EYopwsICk9ZI",
-    "outputId": "1c07d1f3-41bd-47cf-dac7-47f36a158666"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[0.88627071, 0.55624758, 0.97198928, 0.74128787, 0.02940347],\n",
-       "       [0.05604389, 0.22823893, 0.52886436, 0.91998249, 0.01327729],\n",
-       "       [0.74984196, 0.00163448, 0.08632411, 0.08515202, 0.70213274],\n",
-       "       [0.67293052, 0.18162822, 0.38745748, 0.42938446, 0.56581595]])"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.random.rand(4,5)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "6achS2SnlLg6",
-    "outputId": "974f6af6-0fa5-4e1d-f0ab-3c8b85514c78"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "27"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### Generate one random integer in a given range\n",
-    "\n",
-    "np.random.randint(5,50)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "a9WGTceNlmxi",
-    "outputId": "ccd0a4ca-94e2-4249-81d7-c40d4eb1e992"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 6, 44, 15,  7, 34, 32, 38, 20, 16, 27])"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### Generate 10 random integers in a given range\n",
-    "\n",
-    "np.random.randint(5,50,10)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Nkz5qtZ2oUFt",
-    "outputId": "f57e0bae-268a-4a8c-8dba-6d6e89ecb971"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "41"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Random see to output the same random vaues at all run time \n",
-    "import random\n",
-    "\n",
-    "random.seed(10)\n",
-    "\n",
-    "random.randint(5,50)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "k67GJ1K0NDU4"
-   },
-   "source": [
-    "<a name='2'></a>\n",
-    "## 2. Data Selection: Indexing and slicing an Array\n",
-    "\n",
-    "Indexing: Selecting individual elements from the array\n",
-    "\n",
-    "Slicing: Selecting group of element from the array. "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "523qanvFjFD6"
-   },
-   "source": [
-    "\n",
-    "### 2.1 1D Array Indexing and Selection"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {
-    "id": "HEi3p6K5NWqn"
-   },
-   "outputs": [],
-   "source": [
-    "# Creating a 1 dimensional vector\n",
-    "\n",
-    "array_1d = np.array([1,2,3,4,5])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "osAwL_bjNqUa",
-    "outputId": "00bd8764-37cd-43cd-b713-4ad2fd7d4947"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Indexing: selcting an element from an array\n",
-    "\n",
-    "array_1d[1]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "g0CV4DR4Pxrr",
-    "outputId": "03054ff3-f802-41d6-ed9a-948f00d67fd5"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "5"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "\n",
-    "array_1d [-1]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "JROW8R8dNxPb",
-    "outputId": "ad5890d9-a8a6-445b-b5bd-c4a468ddde62"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([3, 4])"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# Slicing: Returning the grou of element from an array\n",
-    "\n",
-    "array_1d [2:4]"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "XCR7_WPnUM2M"
-   },
-   "source": [
-    "### 2.2 2D Array Indexing and Selection"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {
-    "id": "0q6e67_2O60m"
-   },
-   "outputs": [],
-   "source": [
-    "## Indexing 2D array\n",
-    "\n",
-    "array_2d = np.array([[1,2,3],[4,5,6],[7,8,9]])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "5v3HKOHoQP2t",
-    "outputId": "628fe748-a55c-400c-bf31-5a62848574d5"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "5"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Selecting individual element\n",
-    "## array_2d[row][column]\n",
-    "## let's select 5..that is row 1, column 1 (we start from 0!!)\n",
-    "\n",
-    "array_2d[1][1]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "cZhbAnqNR6jQ",
-    "outputId": "78b52c43-6dd0-4254-9e20-51bec4bf5c3c"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "9"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# let's select 9..that is row 2, column 2\n",
-    "\n",
-    "array_2d[2][2]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "B0GnGJCOSDka",
-    "outputId": "31e447b6-3a57-453b-bfc2-bd6050f07632"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([4, 5, 6])"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Selecting whole row\n",
-    "#array_2d[row]\n",
-    "\n",
-    "array_2d[1]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "8OHO4oTHSROF",
-    "outputId": "ee50a860-3233-4fb3-bfa1-a71f2f70ea2e"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3],\n",
-       "       [4, 5, 6]])"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Selecting group of elements in 2D array\n",
-    "## array_2d[rows, columns]..You select rows and columns\n",
-    "\n",
-    "## Let's select the first two rows\n",
-    "## Rows :2 denotes that we are selecting all rows up to the second. \n",
-    "## Columns : denotes that all columns are selected.\n",
-    "\n",
-    "\n",
-    "array_2d[:2,:]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "NIkqcMKr0xoJ",
-    "outputId": "f7895d25-a1ed-4eae-d2d1-624e03541d2b"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2],\n",
-       "       [4, 5]])"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "\n",
-    "## Selecting all first two rows and first two columns\n",
-    "\n",
-    "array_2d[:2,0:2]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "HPwIW3HSTPPu",
-    "outputId": "a3cfa1ba-237b-4201-e6f6-7616b8b4b8da"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3],\n",
-       "       [4, 5, 6]])"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Above is same as\n",
-    "\n",
-    "array_2d[0:2,:]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "hLC6LNsLTdNL",
-    "outputId": "61247100-b491-4a59-95a3-d2d344d83ea7"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3],\n",
-       "       [4, 5, 6],\n",
-       "       [7, 8, 9]])"
-      ]
-     },
-     "execution_count": 35,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## This will return all rows, and so all columns and so same as orginal array\n",
-    "array_2d[0:3,:]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "FNV1X16NUbpJ",
-    "outputId": "7f42ed6b-2ed0-406d-dd47-1907202f0b01"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([7, 8, 9])"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## return the second row\n",
-    "\n",
-    "array_2d[2,:]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "XndtDh1NUmpp",
-    "outputId": "42db9c63-a4c5-47d0-8d9d-b6d7d87b61c3"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([3, 6, 9])"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## return the second column\n",
-    "\n",
-    "array_2d[:,2]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "N9YTUJNjUxdd",
-    "outputId": "08078a90-9fe5-45f6-d618-5ba3a2ea7271"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[2, 3],\n",
-       "       [5, 6],\n",
-       "       [8, 9]])"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## return the last two columns\n",
-    "\n",
-    "array_2d[:,1:3]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "eOcqJEbxU6iR",
-    "outputId": "a0fd909a-5704-42f7-b841-663a943d3f89"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 4, 7])"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## return the first column\n",
-    "\n",
-    "array_2d[:,0]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "OeKEcYRCVKdJ",
-    "outputId": "5b10b5a5-fdf5-47c0-bd2b-d577c51ed1ad"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 2, 3])"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## return the first row\n",
-    "\n",
-    "array_2d[0,:]"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "mgnarYNHVXUT"
-   },
-   "source": [
-    "Indexing or selecting 2D array may seems confusing but when you try it multiple times, you get the idea. If you are selecting an entire row, that means the all the columns are selected (but not their all values). And vice versa. \n",
-    "\n",
-    "As shown below, we are selecting the first row, but as you can see all columns are selected (:).\n",
-    "\n",
-    "```\n",
-    "array_2d[0,:]\n",
-    "```\n",
-    "\n",
-    "\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "zc1Iyb91WHxf"
-   },
-   "source": [
-    "### 2.3 Conditional selection\n",
-    "\n",
-    "You can use a condition to select values in an array. Let's use comparison operators to select the values. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {
-    "id": "ANqjpFENWKCM"
-   },
-   "outputs": [],
-   "source": [
-    "## Let's create an array\n",
-    "\n",
-    "arr= np.array(([1,2,3],[4,5,6],[7,8,9]))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Y9qhO4QaZksn",
-    "outputId": "d31bfcf8-06b8-4b8d-d4da-c6478cd1d58a"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 2, 3, 4, 5])"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Select all elements in an array which are less than 6\n",
-    "\n",
-    "arr[arr <6 ]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "GNY9S75DZusJ",
-    "outputId": "0642da71-f959-4063-8984-83b55e2bd909"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([7, 8, 9])"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Select all elements in an array which are greater than 6\n",
-    "\n",
-    "arr[arr > 6]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "REbbdFOBaBc6",
-    "outputId": "141149de-62ab-4427-ae0a-198117ebda1a"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([2, 4, 6, 8])"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Select all even numbers in an array\n",
-    "\n",
-    "arr[arr % 2 ==0 ]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "ZXeWnQ6maY8A",
-    "outputId": "e8e92e29-2fe7-4c48-9bc5-0bab5cab8a57"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 3, 5, 7, 9])"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Select all odd numbers in an array\n",
-    "\n",
-    "arr[arr % 2 !=0 ]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "TQKfIyGzaeAD",
-    "outputId": "72fa895b-2367-4c56-b3fc-76d07a834d17"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([5, 7, 9])"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## You can also have multiple conditions\n",
-    "\n",
-    "## In all odd numbers, return values which are greater or equal to 5\n",
-    "\n",
-    "\n",
-    "arr[(arr % 2 !=0 ) & (arr >=5) ]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "LvQZsD8UbL2I",
-    "outputId": "dbe32118-6aa3-4b43-ee37-16eff39839e1"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[False, False, False],\n",
-       "       [False, False,  True],\n",
-       "       [ True,  True,  True]])"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Using logical selection, you can also return True for values in which a given condition is met in an array\n",
-    "\n",
-    "arr > 5"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "HGCXwMc-byoh",
-    "outputId": "a8003057-2167-4c15-c240-4c56dcbe3e74"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[False, False, False],\n",
-       "       [False, False, False],\n",
-       "       [False, False, False]])"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## We do not have 0 in our array\n",
-    "\n",
-    "arr == 0"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "kKTlmkV1cM1F"
-   },
-   "source": [
-    "<a name='3'></a>\n",
-    "## 3. Basic Array Operations\n",
-    "\n",
-    "### 3.1 Quick Arithmetic operation: Addition, Subtraction, Multiplication, Division, Squaring"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {
-    "id": "kVyV9yZEcphH"
-   },
-   "outputs": [],
-   "source": [
-    "# Let's create two arrays\n",
-    "\n",
-    "arr1 = np.arange(0,5)\n",
-    "arr2 = np.arange(6,11)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "k-XbCI7DdGSC",
-    "outputId": "b0e463c1-3906-41c7-f98d-ec53596eadc1"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 6,  8, 10, 12, 14])"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Addition\n",
-    "\n",
-    "arr1 + arr2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "HRO_en3BeOEr",
-    "outputId": "afba0120-901e-4c4e-8add-87aa4c326f34"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([6, 6, 6, 6, 6])"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Subtraction\n",
-    "\n",
-    "arr2 - arr1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "nQB3wfgneak3",
-    "outputId": "b1e9b19f-44f5-4298-e478-ff4f07c2a231"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0,  7, 16, 27, 40])"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Multiplication\n",
-    "\n",
-    "arr1 * arr2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "-N1pyoXjej_Y",
-    "outputId": "4ca31127-9cf6-4147-d165-8f51647a3fa0"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0.        , 0.14285714, 0.25      , 0.33333333, 0.4       ])"
-      ]
-     },
-     "execution_count": 53,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Division\n",
-    "\n",
-    "arr1 / arr2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "De6gp_lvetPf",
-    "outputId": "aa0b12f5-ad61-4e88-e2ac-50d79ade09e1"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0,  1,  4,  9, 16])"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Squaring\n",
-    "\n",
-    "arr1 ** 2"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "Ual-ST0-fhCZ"
-   },
-   "source": [
-    "### 3.2 Universal functions\n",
-    "\n",
-    "NumPy universal functions (`ufunc`) allows to compute math, trigonometric, logical and comparison operations such as sin, cos, tan, exponent(exp), log, square, greater, less, etc..."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {
-    "id": "aJfRCWLcfwTr"
-   },
-   "outputs": [],
-   "source": [
-    "## creating two arrays \n",
-    "\n",
-    "arr1 = np.arange(0,5)\n",
-    "arr2 = np.arange(6,11)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "a3QsqIJ4NNxf",
-    "outputId": "094569fa-3458-4022-f4e2-a31aaca28f8e"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 6,  8, 10, 12, 14])"
-      ]
-     },
-     "execution_count": 56,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the sum of two arrays\n",
-    "\n",
-    "np.add(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "43f5eAagNb3J",
-    "outputId": "e9c826cb-26ff-437d-cfe3-191c43fb49f9"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0,  7, 16, 27, 40])"
-      ]
-     },
-     "execution_count": 57,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the product of two arrays\n",
-    "\n",
-    "np.multiply(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "NBG0EPBuNiDZ",
-    "outputId": "3063e564-8824-41cb-f07d-af0b83c1fe0f"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([-6, -6, -6, -6, -6])"
-      ]
-     },
-     "execution_count": 58,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the difference between two arrays\n",
-    "\n",
-    "np.subtract(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "XpgZ6O50NwYa",
-    "outputId": "5578dc8b-be68-4172-ca25-b34fd96afbb1"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0.        , 0.14285714, 0.25      , 0.33333333, 0.4       ])"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the division of two arrays\n",
-    "\n",
-    "np.divide(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "K3Bc6goeHIch",
-    "outputId": "63ea938d-3a71-4066-fc7a-26f8a60ed205"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0.        ,  0.84147098,  0.90929743,  0.14112001, -0.7568025 ])"
-      ]
-     },
-     "execution_count": 60,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the sin of arr1\n",
-    "\n",
-    "np.sin(arr1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Zj05py4IIugZ",
-    "outputId": "6b4eb73e-7d44-4650-81a7-80b5c856d4b1"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 0.        ,  0.85090352,  0.89399666, -0.80115264])"
-      ]
-     },
-     "execution_count": 61,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.sin([0,45,90,180])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "fDo3b-qRIYHR",
-    "outputId": "52ad4b89-32ad-4b80-e430-fc5b337fb25e"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 1.        ,  0.54030231, -0.41614684, -0.9899925 , -0.65364362])"
-      ]
-     },
-     "execution_count": 62,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the cosine of arr 1\n",
-    "\n",
-    "np.cos(arr1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "FsirUyFCIit9",
-    "outputId": "402832da-0a17-4a08-d79d-007ab61a8014"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 1.        ,  0.52532199, -0.44807362, -0.59846007])"
-      ]
-     },
-     "execution_count": 63,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.cos([0,45,90,180])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "XQR8m4HxI1E8",
-    "outputId": "d6434e9b-5527-4466-ac58-6455b3aa15ed"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([-0.29100619,  0.87144798, -6.79971146, -0.45231566,  0.64836083])"
-      ]
-     },
-     "execution_count": 64,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the tangent(tan) of the array\n",
-    "\n",
-    "np.tan(arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "PIOUpa_gJFuv",
-    "outputId": "081b23b0-c74d-4862-b27b-d91cbbffb002"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1.79175947, 1.94591015, 2.07944154, 2.19722458, 2.30258509])"
-      ]
-     },
-     "execution_count": 65,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the logarithmic(log) of the array\n",
-    "\n",
-    "np.log(arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 66,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "b_QsfHLDJVyq",
-    "outputId": "5c73fd2b-3c9a-4921-ab7c-e40b8d20b8c6"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([  403.42879349,  1096.63315843,  2980.95798704,  8103.08392758,\n",
-       "       22026.46579481])"
-      ]
-     },
-     "execution_count": 66,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the exponent(exp or e^) of the array\n",
-    "\n",
-    "np.exp(arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 67,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "s2wDCGMfJfE-",
-    "outputId": "4ed21980-3170-4c47-e1b8-4d268af93560"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([      0,       1,     256,   19683, 1048576])"
-      ]
-     },
-     "execution_count": 67,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the power  of the array\n",
-    "## Array 1 is powered array 2...0^6=0, 1^7=1, 2^8=256, etc..\n",
-    "\n",
-    "np.power(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 68,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "bYGyzm0lKh0b",
-    "outputId": "240eb78c-74db-45e8-f2e2-a314d1e54e2d"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([False, False, False, False, False])"
-      ]
-     },
-     "execution_count": 68,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Comparison operations return true or false\n",
-    "## Arr 1 is less than arr 2...so that's false\n",
-    "\n",
-    "np.greater(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 69,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "rXJJKyJhLfy4",
-    "outputId": "cb9c2426-1068-464c-bae3-f57bf2f5614d"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ True,  True,  True,  True,  True])"
-      ]
-     },
-     "execution_count": 69,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Comparison operations return true or false\n",
-    "## Arr 1 is less than arr 2...so that's true\n",
-    "\n",
-    "np.less(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "6a6Agz1yOAvn"
-   },
-   "source": [
-    "<a name='4'></a>\n",
-    "## 4. Basic Statistics\n",
-    "\n",
-    "With NumPy, we can compute the basic statistics such as the standard deviation (std), variance (var),mean, median, minimum value, maximum value of an array. \n",
-    "\n",
-    "More about NumPy statistics: https://numpy.org/doc/stable/reference/routines.statistics.html#order-statistics"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 70,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "7ZQedUDGHW60",
-    "outputId": "9828d039-3399-4ac4-ff6a-00b5a9b461d4"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4])"
-      ]
-     },
-     "execution_count": 70,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Creating an array \n",
-    "\n",
-    "arr = np.arange(0,5)\n",
-    "arr"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "8eXcY0qjKWtx"
-   },
-   "source": [
-    "### 4.1 Standard Deviation"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 71,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "t-s8L0VJQtpA",
-    "outputId": "716cfeeb-d69b-47e4-cf28-f58fadf1c97b"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1.4142135623730951"
-      ]
-     },
-     "execution_count": 71,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## calculating the standard deviation of the array\n",
-    "## Std is how much an element of the array deviates from the mean of the array\n",
-    "\n",
-    "np.std(arr)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 72,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "PhWndlxuHnrK",
-    "outputId": "608573b6-e1a4-49f6-864b-bfdbc123e578"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1.118033988749895"
-      ]
-     },
-     "execution_count": 72,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr2 = np.array([[3,4], [5,6]])\n",
-    "\n",
-    "np.std(arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 73,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "IH2BFcuZH_jc",
-    "outputId": "530fd53e-1acd-4a70-f401-6f9455641b32"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1., 1.])"
-      ]
-     },
-     "execution_count": 73,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Specifying the axis\n",
-    "## By default, the std is computed on the flattened values (or converted into a single column vector)\n",
-    "\n",
-    "np.std(arr2, axis=0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 74,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "fSCEMvzNIdpZ",
-    "outputId": "691b6163-8eed-4dfc-ae99-72fe0541fea6"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0.5, 0.5])"
-      ]
-     },
-     "execution_count": 74,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.std(arr2, axis=1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "HK8EvjAcKecA"
-   },
-   "source": [
-    "### 4.2 Variance"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 75,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "3DavtYCiIjDY",
-    "outputId": "9735e45c-c03b-40c6-888b-e9da82cd2b55"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2.0"
-      ]
-     },
-     "execution_count": 75,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the Variance (var)\n",
-    "\n",
-    "arr = np.arange(0,5)\n",
-    "\n",
-    "np.var(arr)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 76,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Av4TeSiBI0c9",
-    "outputId": "985ebbf3-f3bc-4604-fae6-e5fee28ec26c"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1.25"
-      ]
-     },
-     "execution_count": 76,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.var(arr2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "B_n2hLsiKq7e"
-   },
-   "source": [
-    "### 4.3 Mean"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 77,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "O1rlEIMiI5aO",
-    "outputId": "a20c288f-9003-43b3-e240-ad33cda96223"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2.0"
-      ]
-     },
-     "execution_count": 77,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the mean of the array\n",
-    "\n",
-    "np.mean(arr)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 78,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "evY84_vLJqe_",
-    "outputId": "1d3571d4-3f8f-477e-bb12-61e2282995d3"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2.0"
-      ]
-     },
-     "execution_count": 78,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## mean gives the same results as the average\n",
-    "np.average(arr)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "xmHcYNRWK0tX"
-   },
-   "source": [
-    "### 4.4 Median"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 79,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "O3ZIMTETJIyk",
-    "outputId": "96fd4a52-04c4-495d-ecf7-f173bc160e1a"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2.0"
-      ]
-     },
-     "execution_count": 79,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the median of the array\n",
-    "\n",
-    "np.median(arr)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "_AkHlz-RK5jP"
-   },
-   "source": [
-    "### 4.3 Minimum and Maximum"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 80,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "XIoaY7s_JoQB",
-    "outputId": "acc350e5-7876-40b2-b5f9-24da2add27ac"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0"
-      ]
-     },
-     "execution_count": 80,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the minimum value\n",
-    "\n",
-    "np.min(arr)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 81,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "mgjxq1w1KAiH",
-    "outputId": "ed372591-6272-43f6-a03b-543785ce58ca"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "4"
-      ]
-     },
-     "execution_count": 81,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Calculating the maximum value\n",
-    "\n",
-    "np.max(arr)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "pZ3JuNw7MwaS"
-   },
-   "source": [
-    "<a name='5'></a>\n",
-    "## 5. Data Manipulation\n",
-    "\n",
-    "Data Manipulation is important step in Machine Learning project. Let's some of NumPy methods and functions which are useful in data manipulation. "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "0TalsnPCkq1X"
-   },
-   "source": [
-    "### 5.1 Shape of the array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 82,
-   "metadata": {
-    "id": "YG_YOgh5kwdL"
-   },
-   "outputs": [],
-   "source": [
-    "## Creating an array \n",
-    "\n",
-    "arr1 = np.arange(0,10)\n",
-    "arr2 = np.array(([1,2,3],[4,5,6],[7,8,9]))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 83,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "cubkv1UCnEbW",
-    "outputId": "f8733420-89e4-4147-f7f9-6525290d9851"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
-      ]
-     },
-     "execution_count": 83,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 84,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "7Q3PRJN3nIZ3",
-    "outputId": "f292d52b-2e0e-4205-d27f-d95570a5e852"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3],\n",
-       "       [4, 5, 6],\n",
-       "       [7, 8, 9]])"
-      ]
-     },
-     "execution_count": 84,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 85,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "YBLLedf7kzJI",
-    "outputId": "3a10664b-70ac-423c-f005-8929979ae309"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(10,)"
-      ]
-     },
-     "execution_count": 85,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.shape(arr1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 86,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "0LoJBrQSk9vk",
-    "outputId": "b15f5438-702b-4cc7-bd9a-0b4665516e31"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(3, 3)"
-      ]
-     },
-     "execution_count": 86,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.shape(arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 87,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "C5vsZtE1lSM2",
-    "outputId": "4cebb28f-dbfa-43c1-83ec-ef07a2580a5e"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(3, 3)"
-      ]
-     },
-     "execution_count": 87,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr2.shape"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "lbjzG0Xrlcbl"
-   },
-   "source": [
-    "### 5.2 Shaping the Array\n",
-    "\n",
-    "`np.reshape(array_name, newshape=(rows, columns)` or `array_name.reshape(rows, columns)` change the shape of the array. The rows and columns of the new shape has to comform with the existing data of the array. Otherwise, it won't work. Take an example, you can convert (3,3) array into (1,9) but you can't convert it into (5,5). "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 88,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "GkU2npH-le_9",
-    "outputId": "a4ac26c0-db89-4b11-e1c9-46dc5a71785f"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[0, 1],\n",
-       "       [2, 3],\n",
-       "       [4, 5],\n",
-       "       [6, 7],\n",
-       "       [8, 9]])"
-      ]
-     },
-     "execution_count": 88,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### arr1 is (10,)....10 rows, 1 column. Let's reshape it into (5,2)\n",
-    "np.reshape(arr1, newshape=(5,2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 89,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "52ls1fjDl9m3",
-    "outputId": "4bdca11e-b2af-4924-de31-24f29863f375"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[0, 1],\n",
-       "       [2, 3],\n",
-       "       [4, 5],\n",
-       "       [6, 7],\n",
-       "       [8, 9]])"
-      ]
-     },
-     "execution_count": 89,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## This would also work\n",
-    "arr1.reshape(5,2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 90,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Mh8_zejvmnRs",
-    "outputId": "f720d0f5-1a55-41ed-c9ca-8d094f8405a2"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3, 4, 5, 6, 7, 8, 9]])"
-      ]
-     },
-     "execution_count": 90,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr2_reshaped = arr2.reshape(9,1)\n",
-    "arr2_reshaped.T"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 91,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "gD1_rWyumsxX",
-    "outputId": "97d95a9f-c806-46e5-86c2-dd660d7465f3"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3],\n",
-       "       [4, 5, 6],\n",
-       "       [7, 8, 9]])"
-      ]
-     },
-     "execution_count": 91,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr2_reshaped.reshape(3,3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 92,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "Iyfh1tWr2VTe",
-    "outputId": "fcbac3c5-86b0-41fd-c37a-eb350e22ce6b"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3, 4, 5, 6, 7, 8, 9]])"
-      ]
-     },
-     "execution_count": 92,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## np.resize can also be used to change the shape of the array into a specific size\n",
-    "\n",
-    "np.resize(arr2, (1,9))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "jPF2gp6PoZK-"
-   },
-   "source": [
-    "### 5.3 Copying array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 93,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "MGacJLaVoZq7",
-    "outputId": "298de278-da88-4f7c-f891-64e37e3b81ea"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
-      ]
-     },
-     "execution_count": 93,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr1 = np.arange(0,10)\n",
-    "arr1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 94,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "ahDMt-anohhh",
-    "outputId": "c65d2739-0914-41b9-9b0c-15e3ae86f2d3"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
-      ]
-     },
-     "execution_count": 94,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr1_copy = arr1.copy()\n",
-    "arr1_copy"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 95,
-   "metadata": {
-    "id": "WQy97R5Wo375"
-   },
-   "outputs": [],
-   "source": [
-    "## Copying the values of one array into the other \n",
-    "\n",
-    "## Let's copy array 2 into 1 --they have the same shape\n",
-    "\n",
-    "arr1 = np.arange(0,6)\n",
-    "arr2 = np.arange(6,12)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 96,
-   "metadata": {
-    "id": "DdE9pVVdppQ8"
-   },
-   "outputs": [],
-   "source": [
-    "## arr1 is destination, arr2 is source\n",
-    "np.copyto(arr1, arr2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 97,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "GhzDAFp2qFgu",
-    "outputId": "801466ef-27ec-4e4d-9678-7b5793356227"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 6,  7,  8,  9, 10, 11])"
-      ]
-     },
-     "execution_count": 97,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr1"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "EScZw0b9rDV-"
-   },
-   "source": [
-    "### 5.4 Joining arrays"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 98,
-   "metadata": {
-    "id": "yVm7cXphrLQD"
-   },
-   "outputs": [],
-   "source": [
-    "### Creating two arrays\n",
-    "\n",
-    "arr1 = np.array([[1,2,3],[4,5,6],[7,8,9]])\n",
-    "arr2 = np.array([[10,11,12]])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 99,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "h5TXwNZErU6g",
-    "outputId": "49113d3c-87dc-4643-8f43-d0be74c5460d"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[ 1,  2,  3],\n",
-       "       [ 4,  5,  6],\n",
-       "       [ 7,  8,  9],\n",
-       "       [10, 11, 12]])"
-      ]
-     },
-     "execution_count": 99,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Joining them\n",
-    "\n",
-    "np.concatenate((arr1, arr2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 100,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "f36TbVcsrVRg",
-    "outputId": "4e785c77-4203-4bee-fe05-cddd8654147c"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[ 1,  2,  3, 10],\n",
-       "       [ 4,  5,  6, 11],\n",
-       "       [ 7,  8,  9, 12]])"
-      ]
-     },
-     "execution_count": 100,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Transposing arr2\n",
-    "## arr2.T is transpose operation\n",
-    "\n",
-    "np.concatenate((arr1, arr2.T), axis=1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 101,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "4XrLudetsvl0",
-    "outputId": "93f316b1-0fa9-4696-9455-395ddc16662b"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12])"
-      ]
-     },
-     "execution_count": 101,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### Setting axis to none flatten the array\n",
-    "\n",
-    "np.concatenate((arr1, arr2), axis=None)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 102,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "bVQMnJais7_6",
-    "outputId": "ab2f34c0-6e2a-49b9-b6fe-1ff22d264289"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[ 0,  6],\n",
-       "       [ 1,  7],\n",
-       "       [ 2,  8],\n",
-       "       [ 3,  9],\n",
-       "       [ 4, 10],\n",
-       "       [ 5, 11]])"
-      ]
-     },
-     "execution_count": 102,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### Joining two 1Ds array into 2D array: Stacking\n",
-    "\n",
-    "# Column stacking\n",
-    "\n",
-    "arr1 = np.arange(0,6)\n",
-    "arr2 = np.arange(6,12)\n",
-    "\n",
-    "np.column_stack((arr1, arr2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 103,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "utJCDp08toet",
-    "outputId": "aad307f9-3caf-448d-cd28-4cc062ef8cc5"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[ 0,  1,  2,  3,  4,  5],\n",
-       "       [ 6,  7,  8,  9, 10, 11]])"
-      ]
-     },
-     "execution_count": 103,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Row stacking \n",
-    "\n",
-    "np.row_stack((arr1, arr2))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "pSk67COOuFJw"
-   },
-   "source": [
-    "### 5.5 Splitting arrays"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 104,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "uPQ3pHuyuJrb",
-    "outputId": "1056b6ad-49ee-4234-cc10-0a7cc2a640b2"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4, 5])"
-      ]
-     },
-     "execution_count": 104,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr1 = np.arange(0,6)\n",
-    "arr1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 105,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "axVESXYzufxz",
-    "outputId": "a3ae64d1-2374-44e2-d99e-ba6113a36b5e"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[array([0, 1, 2]), array([3, 4, 5])]"
-      ]
-     },
-     "execution_count": 105,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### Splitting the array into two arrays\n",
-    "\n",
-    "np.split(arr1, 2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 106,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "NYw7-G0Ovs9u",
-    "outputId": "a15d5f79-a209-401b-9a7d-74e6216acbde"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[array([0, 1]), array([2, 3]), array([4, 5])]"
-      ]
-     },
-     "execution_count": 106,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### Splitting the array into three arrays\n",
-    "\n",
-    "np.split(arr1, 3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "rwOOipKsxEBl"
-   },
-   "source": [
-    "### 5.6 Adding and repeating elements in an array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 107,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "tnDE_kxxxPZI",
-    "outputId": "71daa4f8-fef7-46ba-ea2c-3d6c0d32af58"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4, 5])"
-      ]
-     },
-     "execution_count": 107,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr1 = np.arange(0,6)\n",
-    "arr1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 108,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "qiWApvvXxSyq",
-    "outputId": "e2f29e19-340a-4d2c-b165-1d30d4c5831b"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([0, 1, 2, 3, 4, 5, 7])"
-      ]
-     },
-     "execution_count": 108,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Adding the values at the end of the array\n",
-    "np.append(arr1,7)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 109,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "mzA7NlQKzPN4",
-    "outputId": "e9216924-9372-4b9e-c0e0-3fd174673214"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3, 1, 2, 3, 1, 2, 3]])"
-      ]
-     },
-     "execution_count": 109,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "### Given an array, can you add itself multiple times? or repeat it?\n",
-    "\n",
-    "arr = np.array([[1,2,3]])\n",
-    "np.tile(arr, 3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 110,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "XCkeeaBl0lT4",
-    "outputId": "202b85dd-3f21-408b-ce03-8c9767f116e3"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 1, 1, 2, 2, 2, 3, 3, 3])"
-      ]
-     },
-     "execution_count": 110,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.repeat(arr,3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "3mg3ZMav4HIb"
-   },
-   "source": [
-    "### 5.7 Sorting elements in an array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 111,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "02qT1kUs4L01",
-    "outputId": "5929d293-4a14-4ff8-f543-27ef512c2da7"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 7, 7, 9]])"
-      ]
-     },
-     "execution_count": 111,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "arr = np.array([[1,2,3,4,5,3,2,1,3,5,6,7,7,5,9,5]])\n",
-    "\n",
-    "np.sort(arr)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 112,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "z_b7H94nx61s",
-    "outputId": "dcadd4d3-695c-4a71-c305-f93dda910bb3"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([1, 2, 3, 4, 5, 6, 7, 9])"
-      ]
-     },
-     "execution_count": 112,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Finding the unique elements in an array\n",
-    "\n",
-    "arr = np.array([[1,2,3,4,5,3,2,1,3,5,6,7,7,5,9,5]])\n",
-    "\n",
-    "np.unique(arr)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "assBn6MPAOaW"
-   },
-   "source": [
-    "### 5.8 Reversing an array"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 113,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "E1aycT_l1Acu",
-    "outputId": "e9145b3f-7f68-4d95-8d81-34f959c17fbb"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1, 2, 3],\n",
-       "       [4, 5, 6],\n",
-       "       [7, 8, 9]])"
-      ]
-     },
-     "execution_count": 113,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## You can also flip the array\n",
-    "\n",
-    "arr = np.array([[1,2,3],[4,5,6],[7,8,9]])\n",
-    "arr"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 114,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "5DwhyTxY17Wx",
-    "outputId": "d255183a-eb16-4117-ea35-31439a19840b"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[7, 8, 9],\n",
-       "       [4, 5, 6],\n",
-       "       [1, 2, 3]])"
-      ]
-     },
-     "execution_count": 114,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## Up/down flipping\n",
-    "\n",
-    "np.flipud(arr)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 115,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/"
-    },
-    "id": "XQTBiI5m19gh",
-    "outputId": "215de3e1-9884-44be-c7b2-93e09803ee15"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[3, 2, 1],\n",
-       "       [6, 5, 4],\n",
-       "       [9, 8, 7]])"
-      ]
-     },
-     "execution_count": 115,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "## left/right flipping\n",
-    "\n",
-    "np.fliplr(arr)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "mBh5uGjL4ZBq"
-   },
-   "source": [
-    "\n",
-    "\n",
-    "---\n",
-    "\n",
-    "\n",
-    "\n",
-    "---\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "id": "dIRTQbdH2wzC"
-   },
-   "source": [
-    "That's it for NumPy. In this lab, you learned how to create an array, perform basic operations, and also how to manipulate an array. \n",
-    "\n",
-    "It's kind of fascinating to think how tools like `TensorFlow, Sklearn, Pandas....` are powered by NumPy. \n",
-    "\n",
-    "In the next lab, we will learn about the Pandas, another important tool used for real world data manipulation."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "colab": {
-   "name": "1. Intro to NumPy for Data Computation.ipynb",
-   "provenance": []
-  },
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.7.10"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}