07.Matrices.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     [,1] [,2] [,3]\n",
      "[1,]    3    4    5\n",
      "[2,]    6    7    8\n",
      "[3,]    9   10   11\n",
      "[4,]   12   13   14\n"
     ]
    }
   ],
   "source": [
    "M <- matrix(c(3:14), nrow = 4, byrow = TRUE)\n",
    "print(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in matrix(c(1:9), nrow = 4, byrow = TRUE):\n",
      "“data length [9] is not a sub-multiple or multiple of the number of rows [4]”\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     [,1] [,2] [,3]\n",
      "[1,]    1    2    3\n",
      "[2,]    4    5    6\n",
      "[3,]    7    8    9\n",
      "[4,]    1    2    3\n"
     ]
    }
   ],
   "source": [
    "M <- matrix(c(1:9), nrow = 4, byrow = TRUE)\n",
    "print(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     [,1] [,2] [,3]\n",
      "[1,]    1    2    3\n",
      "[2,]    4    5    6\n",
      "[3,]    7    8    9\n",
      "[4,]   10   11   12\n"
     ]
    }
   ],
   "source": [
    "M <- matrix(c(1:12), nrow = 4, byrow = TRUE)\n",
    "print(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     [,1] [,2] [,3]\n",
      "[1,]    3    7   11\n",
      "[2,]    4    8   12\n",
      "[3,]    5    9   13\n",
      "[4,]    6   10   14\n"
     ]
    }
   ],
   "source": [
    "N <- matrix(c(3:14), nrow = 4, byrow = FALSE)\n",
    "print(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "rownames = c(\"row1\", \"row2\", \"row3\", \"row4\")\n",
    "colnames = c(\"col1\", \"col2\", \"col3\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     col1 col2 col3\n",
      "row1    3    4    5\n",
      "row2    6    7    8\n",
      "row3    9   10   11\n",
      "row4   12   13   14\n"
     ]
    }
   ],
   "source": [
    "P <- matrix(c(3:14), nrow = 4, byrow = TRUE, dimnames = list(rownames, colnames))\n",
    "print(P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the column and row names.\n",
    "rownames = c(\"row1\", \"row2\", \"row3\", \"row4\")\n",
    "colnames = c(\"col1\", \"col2\", \"col3\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create the matrix.\n",
    "P <- matrix(c(3:14), nrow = 4, byrow = TRUE, dimnames = list(rownames, colnames))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] 5\n"
     ]
    }
   ],
   "source": [
    "# Access the element at 3rd column and 1st row.\n",
    "print(P[1,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] 13\n"
     ]
    }
   ],
   "source": [
    "# Access the element at 2nd column and 4th row.\n",
    "print(P[4,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "col1 col2 col3 \n",
      "   6    7    8 \n",
      "row1 row2 row3 row4 \n",
      "   5    8   11   14 \n"
     ]
    }
   ],
   "source": [
    "# Access only the  2nd row.\n",
    "print(P[2,])\n",
    "\n",
    "# Access only the 3rd column.\n",
    "print(P[,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     [,1] [,2] [,3]\n",
      "[1,]    3   -1    2\n",
      "[2,]    9    4    6\n"
     ]
    }
   ],
   "source": [
    "# Create two 2x3 matrices.\n",
    "matrix1 <- matrix(c(3, 9, -1, 4, 2, 6), nrow = 2)\n",
    "print(matrix1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     [,1] [,2] [,3]\n",
      "[1,]    5    0    3\n",
      "[2,]    2    9    4\n"
     ]
    }
   ],
   "source": [
    "matrix2 <- matrix(c(5, 2, 0, 9, 3, 4), nrow = 2)\n",
    "print(matrix2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result of addition \n",
      "     [,1] [,2] [,3]\n",
      "[1,]    8   -1    5\n",
      "[2,]   11   13   10\n"
     ]
    }
   ],
   "source": [
    "# Add the matrices.\n",
    "result <- matrix1 + matrix2\n",
    "cat(\"Result of addition\",\"\\n\")\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result of subtraction \n",
      "     [,1] [,2] [,3]\n",
      "[1,]   -2   -1   -1\n",
      "[2,]    7   -5    2\n"
     ]
    }
   ],
   "source": [
    "# Subtract the matrices\n",
    "result <- matrix1 - matrix2\n",
    "cat(\"Result of subtraction\",\"\\n\")\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     [,1] [,2] [,3]\n",
      "[1,]    3   -1    2\n",
      "[2,]    9    4    6\n"
     ]
    }
   ],
   "source": [
    "# Create two 2x3 matrices.\n",
    "matrix1 <- matrix(c(3, 9, -1, 4, 2, 6), nrow = 2)\n",
    "print(matrix1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     [,1] [,2] [,3]\n",
      "[1,]    5    0    3\n",
      "[2,]    2    9    4\n"
     ]
    }
   ],
   "source": [
    "matrix2 <- matrix(c(5, 2, 0, 9, 3, 4), nrow = 2)\n",
    "print(matrix2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result of multiplication \n",
      "     [,1] [,2] [,3]\n",
      "[1,]   15    0    6\n",
      "[2,]   18   36   24\n"
     ]
    }
   ],
   "source": [
    "# Multiply the matrices.\n",
    "result <- matrix1 * matrix2\n",
    "cat(\"Result of multiplication\",\"\\n\")\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result of division \n",
      "     [,1]      [,2]      [,3]\n",
      "[1,]  0.6      -Inf 0.6666667\n",
      "[2,]  4.5 0.4444444 1.5000000\n"
     ]
    }
   ],
   "source": [
    "# Divide the matrices\n",
    "result <- matrix1 / matrix2\n",
    "cat(\"Result of division\",\"\\n\")\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=matrix(1:9, nrow = 3, ncol = 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 3 × 3 of type int</caption>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>4</td><td>7</td></tr>\n",
       "\t<tr><td>2</td><td>5</td><td>8</td></tr>\n",
       "\t<tr><td>3</td><td>6</td><td>9</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type int\n",
       "\\begin{tabular}{lll}\n",
       "\t 1 & 4 & 7\\\\\n",
       "\t 2 & 5 & 8\\\\\n",
       "\t 3 & 6 & 9\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type int\n",
       "\n",
       "| 1 | 4 | 7 |\n",
       "| 2 | 5 | 8 |\n",
       "| 3 | 6 | 9 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 1    4    7   \n",
       "[2,] 2    5    8   \n",
       "[3,] 3    6    9   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "b=matrix(11,19, nrow = 3, ncol = 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 3 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>11</td><td>11</td><td>11</td></tr>\n",
       "\t<tr><td>11</td><td>11</td><td>11</td></tr>\n",
       "\t<tr><td>11</td><td>11</td><td>11</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type dbl\n",
       "\\begin{tabular}{lll}\n",
       "\t 11 & 11 & 11\\\\\n",
       "\t 11 & 11 & 11\\\\\n",
       "\t 11 & 11 & 11\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type dbl\n",
       "\n",
       "| 11 | 11 | 11 |\n",
       "| 11 | 11 | 11 |\n",
       "| 11 | 11 | 11 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 11   11   11  \n",
       "[2,] 11   11   11  \n",
       "[3,] 11   11   11  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 3 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>12</td><td>15</td><td>18</td></tr>\n",
       "\t<tr><td>13</td><td>16</td><td>19</td></tr>\n",
       "\t<tr><td>14</td><td>17</td><td>20</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type dbl\n",
       "\\begin{tabular}{lll}\n",
       "\t 12 & 15 & 18\\\\\n",
       "\t 13 & 16 & 19\\\\\n",
       "\t 14 & 17 & 20\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type dbl\n",
       "\n",
       "| 12 | 15 | 18 |\n",
       "| 13 | 16 | 19 |\n",
       "| 14 | 17 | 20 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 12   15   18  \n",
       "[2,] 13   16   19  \n",
       "[3,] 14   17   20  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 3 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>11</td><td>44</td><td>77</td></tr>\n",
       "\t<tr><td>22</td><td>55</td><td>88</td></tr>\n",
       "\t<tr><td>33</td><td>66</td><td>99</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type dbl\n",
       "\\begin{tabular}{lll}\n",
       "\t 11 & 44 & 77\\\\\n",
       "\t 22 & 55 & 88\\\\\n",
       "\t 33 & 66 & 99\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type dbl\n",
       "\n",
       "| 11 | 44 | 77 |\n",
       "| 22 | 55 | 88 |\n",
       "| 33 | 66 | 99 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 11   44   77  \n",
       "[2,] 22   55   88  \n",
       "[3,] 33   66   99  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x*b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 3 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>-10</td><td>-7</td><td>-4</td></tr>\n",
       "\t<tr><td> -9</td><td>-6</td><td>-3</td></tr>\n",
       "\t<tr><td> -8</td><td>-5</td><td>-2</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type dbl\n",
       "\\begin{tabular}{lll}\n",
       "\t -10 & -7 & -4\\\\\n",
       "\t  -9 & -6 & -3\\\\\n",
       "\t  -8 & -5 & -2\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type dbl\n",
       "\n",
       "| -10 | -7 | -4 |\n",
       "|  -9 | -6 | -3 |\n",
       "|  -8 | -5 | -2 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] -10  -7   -4  \n",
       "[2,]  -9  -6   -3  \n",
       "[3,]  -8  -5   -2  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x-b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 3 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>0.09090909</td><td>0.3636364</td><td>0.6363636</td></tr>\n",
       "\t<tr><td>0.18181818</td><td>0.4545455</td><td>0.7272727</td></tr>\n",
       "\t<tr><td>0.27272727</td><td>0.5454545</td><td>0.8181818</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type dbl\n",
       "\\begin{tabular}{lll}\n",
       "\t 0.09090909 & 0.3636364 & 0.6363636\\\\\n",
       "\t 0.18181818 & 0.4545455 & 0.7272727\\\\\n",
       "\t 0.27272727 & 0.5454545 & 0.8181818\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type dbl\n",
       "\n",
       "| 0.09090909 | 0.3636364 | 0.6363636 |\n",
       "| 0.18181818 | 0.4545455 | 0.7272727 |\n",
       "| 0.27272727 | 0.5454545 | 0.8181818 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1]       [,2]      [,3]     \n",
       "[1,] 0.09090909 0.3636364 0.6363636\n",
       "[2,] 0.18181818 0.4545455 0.7272727\n",
       "[3,] 0.27272727 0.5454545 0.8181818"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x/b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'matrix'"
      ],
      "text/latex": [
       "'matrix'"
      ],
      "text/markdown": [
       "'matrix'"
      ],
      "text/plain": [
       "[1] \"matrix\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre class=language-r><code>.Primitive(\"dim\")</code></pre>"
      ],
      "text/latex": [
       "\\begin{minted}{r}\n",
       ".Primitive(\"dim\")\n",
       "\\end{minted}"
      ],
      "text/markdown": [
       "```r\n",
       ".Primitive(\"dim\")\n",
       "```"
      ],
      "text/plain": [
       "function (x)  .Primitive(\"dim\")"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>3</li><li>3</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 3\n",
       "2. 3\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 3 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>3</li><li>3</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 3\n",
       "2. 3\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 3 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "a=matrix(1:9, nrow = 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 3 × 3 of type int</caption>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>4</td><td>7</td></tr>\n",
       "\t<tr><td>2</td><td>5</td><td>8</td></tr>\n",
       "\t<tr><td>3</td><td>6</td><td>9</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type int\n",
       "\\begin{tabular}{lll}\n",
       "\t 1 & 4 & 7\\\\\n",
       "\t 2 & 5 & 8\\\\\n",
       "\t 3 & 6 & 9\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type int\n",
       "\n",
       "| 1 | 4 | 7 |\n",
       "| 2 | 5 | 8 |\n",
       "| 3 | 6 | 9 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 1    4    7   \n",
       "[2,] 2    5    8   \n",
       "[3,] 3    6    9   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "x <- matrix(1:9, nrow = 3, dimnames = list(c(\"X\",\"Y\",\"Z\"), c(\"A\",\"B\",\"C\")))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 3 × 3 of type int</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>A</th><th scope=col>B</th><th scope=col>C</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X</th><td>1</td><td>4</td><td>7</td></tr>\n",
       "\t<tr><th scope=row>Y</th><td>2</td><td>5</td><td>8</td></tr>\n",
       "\t<tr><th scope=row>Z</th><td>3</td><td>6</td><td>9</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type int\n",
       "\\begin{tabular}{r|lll}\n",
       "  & A & B & C\\\\\n",
       "\\hline\n",
       "\tX & 1 & 4 & 7\\\\\n",
       "\tY & 2 & 5 & 8\\\\\n",
       "\tZ & 3 & 6 & 9\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type int\n",
       "\n",
       "| <!--/--> | A | B | C |\n",
       "|---|---|---|---|\n",
       "| X | 1 | 4 | 7 |\n",
       "| Y | 2 | 5 | 8 |\n",
       "| Z | 3 | 6 | 9 |\n",
       "\n"
      ],
      "text/plain": [
       "  A B C\n",
       "X 1 4 7\n",
       "Y 2 5 8\n",
       "Z 3 6 9"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'A'</li><li>'B'</li><li>'C'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'A'\n",
       "\\item 'B'\n",
       "\\item 'C'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'A'\n",
       "2. 'B'\n",
       "3. 'C'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"A\" \"B\" \"C\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colnames(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'X'</li><li>'Y'</li><li>'Z'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'X'\n",
       "\\item 'Y'\n",
       "\\item 'Z'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'X'\n",
       "2. 'Y'\n",
       "3. 'Z'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"X\" \"Y\" \"Z\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rownames(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 3 × 2 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>4</td></tr>\n",
       "\t<tr><td>2</td><td>5</td></tr>\n",
       "\t<tr><td>3</td><td>6</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 2 of type dbl\n",
       "\\begin{tabular}{ll}\n",
       "\t 1 & 4\\\\\n",
       "\t 2 & 5\\\\\n",
       "\t 3 & 6\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 2 of type dbl\n",
       "\n",
       "| 1 | 4 |\n",
       "| 2 | 5 |\n",
       "| 3 | 6 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2]\n",
       "[1,] 1    4   \n",
       "[2,] 2    5   \n",
       "[3,] 3    6   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cbind(c(1,2,3),c(4,5,6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "x <- c(1,2,3,4,5,6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'numeric'"
      ],
      "text/latex": [
       "'numeric'"
      ],
      "text/markdown": [
       "'numeric'"
      ],
      "text/plain": [
       "[1] \"numeric\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 2 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>3</td><td>5</td></tr>\n",
       "\t<tr><td>2</td><td>4</td><td>6</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 3 of type dbl\n",
       "\\begin{tabular}{lll}\n",
       "\t 1 & 3 & 5\\\\\n",
       "\t 2 & 4 & 6\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 3 of type dbl\n",
       "\n",
       "| 1 | 3 | 5 |\n",
       "| 2 | 4 | 6 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 1    3    5   \n",
       "[2,] 2    4    6   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(x) <- c(2,3)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'matrix'"
      ],
      "text/latex": [
       "'matrix'"
      ],
      "text/markdown": [
       "'matrix'"
      ],
      "text/plain": [
       "[1] \"matrix\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 2 × 2 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>3</td><td>5</td></tr>\n",
       "\t<tr><td>4</td><td>6</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 2 of type dbl\n",
       "\\begin{tabular}{ll}\n",
       "\t 3 & 5\\\\\n",
       "\t 4 & 6\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 2 of type dbl\n",
       "\n",
       "| 3 | 5 |\n",
       "| 4 | 6 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2]\n",
       "[1,] 3    5   \n",
       "[2,] 4    6   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x[c(1,2),c(2,3)] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 2 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>3</td><td>5</td></tr>\n",
       "\t<tr><td>2</td><td>4</td><td>6</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 3 of type dbl\n",
       "\\begin{tabular}{lll}\n",
       "\t 1 & 3 & 5\\\\\n",
       "\t 2 & 4 & 6\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 3 of type dbl\n",
       "\n",
       "| 1 | 3 | 5 |\n",
       "| 2 | 4 | 6 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 1    3    5   \n",
       "[2,] 2    4    6   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x[,] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 2 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>3</td><td>5</td></tr>\n",
       "\t<tr><td>2</td><td>4</td><td>6</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 3 of type dbl\n",
       "\\begin{tabular}{lll}\n",
       "\t 1 & 3 & 5\\\\\n",
       "\t 2 & 4 & 6\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 3 of type dbl\n",
       "\n",
       "| 1 | 3 | 5 |\n",
       "| 2 | 4 | 6 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 1    3    5   \n",
       "[2,] 2    4    6   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x[,] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>2</li><li>4</li><li>6</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2\n",
       "\\item 4\n",
       "\\item 6\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2\n",
       "2. 4\n",
       "3. 6\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 2 4 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x[-1,] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>1</li><li>3</li><li>5</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 5\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 3\n",
       "3. 5\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 3 5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x[1,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 1 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>3</td><td>5</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 1 × 3 of type dbl\n",
       "\\begin{tabular}{lll}\n",
       "\t 1 & 3 & 5\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 1 × 3 of type dbl\n",
       "\n",
       "| 1 | 3 | 5 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 1    3    5   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x[1,,drop=FALSE] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'matrix'"
      ],
      "text/latex": [
       "'matrix'"
      ],
      "text/markdown": [
       "'matrix'"
      ],
      "text/plain": [
       "[1] \"matrix\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class(x[1,,drop=FALSE])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'matrix'"
      ],
      "text/latex": [
       "'matrix'"
      ],
      "text/markdown": [
       "'matrix'"
      ],
      "text/plain": [
       "[1] \"matrix\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>1</li><li>2</li><li>3</li><li>4</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 2\n",
       "3. 3\n",
       "4. 4\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 2 3 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x[1:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>1</li><li>3</li><li>5</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 5\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 3\n",
       "3. 5\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 3 5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x[c(TRUE, FALSE)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "6"
      ],
      "text/latex": [
       "6"
      ],
      "text/markdown": [
       "6"
      ],
      "text/plain": [
       "[1] 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x[x>5] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>2</li><li>4</li><li>6</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2\n",
       "\\item 4\n",
       "\\item 6\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2\n",
       "2. 4\n",
       "3. 6\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 2 4 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    " x[x%%2 == 0] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>X</dt><dd>1</dd><dt>Y</dt><dd>2</dd><dt>Z</dt><dd>3</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[X] 1\n",
       "\\item[Y] 2\n",
       "\\item[Z] 3\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "X\n",
       ":   1Y\n",
       ":   2Z\n",
       ":   3\n",
       "\n"
      ],
      "text/plain": [
       "X Y Z \n",
       "1 2 3 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- matrix(1:9, nrow = 3, dimnames = list(c(\"X\",\"Y\",\"Z\"), c(\"A\",\"B\",\"C\")))\n",
    "x[,\"A\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 3 × 2 of type int</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>A</th><th scope=col>C</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X</th><td>1</td><td>7</td></tr>\n",
       "\t<tr><th scope=row>Y</th><td>2</td><td>8</td></tr>\n",
       "\t<tr><th scope=row>Z</th><td>3</td><td>9</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 2 of type int\n",
       "\\begin{tabular}{r|ll}\n",
       "  & A & C\\\\\n",
       "\\hline\n",
       "\tX & 1 & 7\\\\\n",
       "\tY & 2 & 8\\\\\n",
       "\tZ & 3 & 9\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 2 of type int\n",
       "\n",
       "| <!--/--> | A | C |\n",
       "|---|---|---|\n",
       "| X | 1 | 7 |\n",
       "| Y | 2 | 8 |\n",
       "| Z | 3 | 9 |\n",
       "\n"
      ],
      "text/plain": [
       "  A C\n",
       "X 1 7\n",
       "Y 2 8\n",
       "Z 3 9"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x[TRUE,c(\"A\",\"C\")]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 2 × 2 of type int</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>A</th><th scope=col>C</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Y</th><td>2</td><td>8</td></tr>\n",
       "\t<tr><th scope=row>Z</th><td>3</td><td>9</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 2 of type int\n",
       "\\begin{tabular}{r|ll}\n",
       "  & A & C\\\\\n",
       "\\hline\n",
       "\tY & 2 & 8\\\\\n",
       "\tZ & 3 & 9\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 2 of type int\n",
       "\n",
       "| <!--/--> | A | C |\n",
       "|---|---|---|\n",
       "| Y | 2 | 8 |\n",
       "| Z | 3 | 9 |\n",
       "\n"
      ],
      "text/plain": [
       "  A C\n",
       "Y 2 8\n",
       "Z 3 9"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x[2:3,c(\"A\",\"C\")]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "x[2,2] <- 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "x[x<5] <- 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 3 × 3 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>X</th><th scope=col>Y</th><th scope=col>Z</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>A</th><td>0</td><td> 0</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>B</th><td>0</td><td>10</td><td>6</td></tr>\n",
       "\t<tr><th scope=row>C</th><td>7</td><td> 8</td><td>9</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type dbl\n",
       "\\begin{tabular}{r|lll}\n",
       "  & X & Y & Z\\\\\n",
       "\\hline\n",
       "\tA & 0 &  0 & 0\\\\\n",
       "\tB & 0 & 10 & 6\\\\\n",
       "\tC & 7 &  8 & 9\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type dbl\n",
       "\n",
       "| <!--/--> | X | Y | Z |\n",
       "|---|---|---|---|\n",
       "| A | 0 |  0 | 0 |\n",
       "| B | 0 | 10 | 6 |\n",
       "| C | 7 |  8 | 9 |\n",
       "\n"
      ],
      "text/plain": [
       "  X Y  Z\n",
       "A 0  0 0\n",
       "B 0 10 6\n",
       "C 7  8 9"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t(x)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 3 × 4 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>A</th><th scope=col>B</th><th scope=col>C</th><th scope=col></th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X</th><td>0</td><td> 0</td><td>7</td><td>1</td></tr>\n",
       "\t<tr><th scope=row>Y</th><td>0</td><td>10</td><td>8</td><td>2</td></tr>\n",
       "\t<tr><th scope=row>Z</th><td>0</td><td> 6</td><td>9</td><td>3</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 4 of type dbl\n",
       "\\begin{tabular}{r|llll}\n",
       "  & A & B & C & \\\\\n",
       "\\hline\n",
       "\tX & 0 &  0 & 7 & 1\\\\\n",
       "\tY & 0 & 10 & 8 & 2\\\\\n",
       "\tZ & 0 &  6 & 9 & 3\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 4 of type dbl\n",
       "\n",
       "| <!--/--> | A | B | C | <!----> |\n",
       "|---|---|---|---|---|\n",
       "| X | 0 |  0 | 7 | 1 |\n",
       "| Y | 0 | 10 | 8 | 2 |\n",
       "| Z | 0 |  6 | 9 | 3 |\n",
       "\n"
      ],
      "text/plain": [
       "  A B  C  \n",
       "X 0  0 7 1\n",
       "Y 0 10 8 2\n",
       "Z 0  6 9 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cbind(x, c(1, 2, 3)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 4 × 3 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>A</th><th scope=col>B</th><th scope=col>C</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X</th><td>0</td><td> 0</td><td>7</td></tr>\n",
       "\t<tr><th scope=row>Y</th><td>0</td><td>10</td><td>8</td></tr>\n",
       "\t<tr><th scope=row>Z</th><td>0</td><td> 6</td><td>9</td></tr>\n",
       "\t<tr><th scope=row></th><td>1</td><td> 2</td><td>3</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 4 × 3 of type dbl\n",
       "\\begin{tabular}{r|lll}\n",
       "  & A & B & C\\\\\n",
       "\\hline\n",
       "\tX & 0 &  0 & 7\\\\\n",
       "\tY & 0 & 10 & 8\\\\\n",
       "\tZ & 0 &  6 & 9\\\\\n",
       "\t & 1 &  2 & 3\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 4 × 3 of type dbl\n",
       "\n",
       "| <!--/--> | A | B | C |\n",
       "|---|---|---|---|\n",
       "| X | 0 |  0 | 7 |\n",
       "| Y | 0 | 10 | 8 |\n",
       "| Z | 0 |  6 | 9 |\n",
       "| <!----> | 1 |  2 | 3 |\n",
       "\n"
      ],
      "text/plain": [
       "  A B  C\n",
       "X 0  0 7\n",
       "Y 0 10 8\n",
       "Z 0  6 9\n",
       "  1  2 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    " rbind(x,c(1,2,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 2 × 3 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>A</th><th scope=col>B</th><th scope=col>C</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X</th><td>0</td><td> 0</td><td>7</td></tr>\n",
       "\t<tr><th scope=row>Y</th><td>0</td><td>10</td><td>8</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 3 of type dbl\n",
       "\\begin{tabular}{r|lll}\n",
       "  & A & B & C\\\\\n",
       "\\hline\n",
       "\tX & 0 &  0 & 7\\\\\n",
       "\tY & 0 & 10 & 8\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 3 of type dbl\n",
       "\n",
       "| <!--/--> | A | B | C |\n",
       "|---|---|---|---|\n",
       "| X | 0 |  0 | 7 |\n",
       "| Y | 0 | 10 | 8 |\n",
       "\n"
      ],
      "text/plain": [
       "  A B  C\n",
       "X 0  0 7\n",
       "Y 0 10 8"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    " x <- x[1:2,]; x  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 3 × 2 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>10</td></tr>\n",
       "\t<tr><td>0</td><td> 7</td></tr>\n",
       "\t<tr><td>0</td><td> 8</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 2 of type dbl\n",
       "\\begin{tabular}{ll}\n",
       "\t 0 & 10\\\\\n",
       "\t 0 &  7\\\\\n",
       "\t 0 &  8\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 2 of type dbl\n",
       "\n",
       "| 0 | 10 |\n",
       "| 0 |  7 |\n",
       "| 0 |  8 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2]\n",
       "[1,] 0    10  \n",
       "[2,] 0     7  \n",
       "[3,] 0     8  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(x) <- c(3,2); x "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] 1 6\n"
     ]
    }
   ],
   "source": [
    "print(dim(x) <- c(1,6))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R 4",
   "language": "R",
   "name": "ir33"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}