From abaea2d7482b501600def76702093c6f0a041d75 Mon Sep 17 00:00:00 2001 From: esha Date: Thu, 3 Feb 2022 23:51:47 +0530 Subject: [PATCH 1/3] added questions for lec8 --- Selected Questions/Images/lec8_a1.png | Bin 0 -> 1972 bytes Selected Questions/Images/lec8_a2.png | Bin 0 -> 4058 bytes Selected Questions/Images/lec8_q2.png | Bin 0 -> 7009 bytes Selected Questions/lec8.md | 33 ++++++++++++++++++++++++++ 4 files changed, 33 insertions(+) create mode 100644 Selected Questions/Images/lec8_a1.png create mode 100644 Selected Questions/Images/lec8_a2.png create mode 100644 Selected Questions/Images/lec8_q2.png create mode 100644 Selected Questions/lec8.md diff --git a/Selected Questions/Images/lec8_a1.png b/Selected Questions/Images/lec8_a1.png new file mode 100644 index 0000000000000000000000000000000000000000..4cc9c93671bd023ad5dd610953a9b8c1c8820b1d GIT binary patch literal 1972 zcmV;l2TS;gP)Px#1ZP1_K>z@;j|==^1poj532;bRa{vGmbN~PnbOGLGA9w%&2T4gpK~!i%?V5XR zjb|Lk>$bnPi26tUK}f_>*Cs?%M6Ff2h*F(ff(e3PVY7>CRg76>1Z~x27POU^TM&lD zl#x*FXjiSqrs#@ww4GaN`|h*f@A2-O)Ap!3Waa(j{p0;T&vVZEe4q3DF3&l~&w5jF zl)rg6%HKR3SWFCHv(>eQ)i+qTD#AJ=vkeg6FU&6_trBxs`- zZr{F*3me0`^2EeMV+*HGpN@%%;TbGH>j&Dtbm>xE2sM2R51lb%hA}KFJUl!gAfQ~p zOixd5+_;sJR5>p;wmUqdyTCoQL2z)ewnJ1@6yo)M(xgez(b0PEN>zE;_bK0Ttxrr$z@uD9 zh>zc#y7xh)#pMcB1B8TxY}~lfG)Z7@+O#PJm73ePZ|~f>^Mwl+HgDeit$=T8mxA)S zbLSevyK>h^=t^2znys8Pla!RC?M%Yo-=93B=9x2R5U=+yi0-MACr_%GD{z|X)2ENN zKww}Xd54X_J#ijZuU@TPilf|6C*|sdR1_TaaGv4Aho=a5SId?y@n?!>2n`K&-Hk_& z9vv}agfZ$1o179=t7Gb@1q&98A3vV58ioxUModBKM*>e*+2n0vJ}^>KfP!+~${2N2 zj`INNghGvVwc{3*^YZ1(=ggVINf12B7?gW>T0JN%ESx%Zs?LXC#so%>9?g*nm>y|t z_UzeRlC9i3T0&O`Ph)0mS7W~f*xnpJjUimR zbcy()^(?+d^P4YOA1X!%_YM%FD{is1_h3B*ZlN6sMNtXB%LCpaJ254EnW5*6oogB`z{h4sEi;9Y}e*_;NW1Q9bi^gR(9>$^?hO6wrza!g9Z)KkO|B+gH0-`q*Vq%OTunIkU_B4iN zvC6ES-f!5jfrO{`HR33*uX1ujhYlUm1`kKYw1=f-Y8>`igu8 z+G2xK%$haJ7&Sp@gtOSMa+JG66oK0Ed2LYqY~8w*`iCG7ru9|96T5ZmmYtn#>}sHV zzXd!PGiHpPbR6aGEEjMaoTsd;4BrOR z*U(_*|NeWfy!_g=YyJB5vwvx;S-GB&+q7xZy?b|xBr+M8zJ|uZg9ka)0JUbvjvejO zw4>Y|3O%46L@?Wf8URdRLj!NszlY}K<+&!pnw7u)Sk^z*b>90tiZ6Ho0000Px#1ZP1_K>z@;j|==^1poj532;bRa{vGmbN~PnbOGLGA9w%&4{u3CK~#8N?VNd3 zRAnE>J=Gs?d903Bu4!h+B|`;VK}9);U;!0J3Ad62WK%>I1r-!fA$(C06jTfq6j8`j z(!nJ#Km<(?BvBCAkws(~6cFAoJkN~7%$|=RQNfwl~4O zq&QFCgZx+2WI^Pi{bAA9Td4J#>f%RU9^Ma%pHchY%$w2XaZXPC%T{Wzq$&Mw=F3;& zf269Ups?)!K^X96wCO_;`n2i2Flf`-+WO$ZgVfa2`1ts^xVYThTzaCHfj9QsZ@>NC zK~ho@-ZnkK38kf_e|K=})~%wVB6?IFRaI3P85soy1^M~;^pJEIv}tN;8asBZwzl@d zg$w7+o9F52Nl)}L+}+)W3>h+X=+KWo`e@v^am~%m^aLk3I5-R%H0Z+*KYZ`K_dGm2 z=uvsxxN&3T$dMB#PQ>lCwzf`APNpZAV9*91^2;y3yng*UwFO{eg8KUUr%#{4EGa2T zNJyxxtR!cZLQ6}_t5>h9H<;Dc)wQ*?)b0$dGZ9_)6mc`efso>hzNRu2?lNWeEyg*W1uj#JGg)U{;*-g1`i%QaNxj8 zmoDK5BFS5Cy%iG^LoVn(`}gn1gu=8seE2XqlAWDBckWzEOG{!(15rg?U7cfX%+1aB z?b}BUnUt58A2@K}?%li87NDo6clz{cYB0f|4Q4JR{qxU1sog<9K!Bg0AASY}1!2PC zNMT`N|Ni|EaLEPTUMT^{rdI0bLS2@ZfIyIH>jqirNM9DK-A`h)vH%4 zq7D2W9)?eJ{``4*NB~ksm$d?-@A8@9%^eldGh4&;lnE` zDiGO7lw*Ofa0f9#$i?hHAf}_X zw#kzx6R$(Ui`iB4{O#~7#JV`GC7fS9_vy0d4`CSw$= zs1bm(v$L9-T6%gqIS!x=@(n@p!VN;4`1p7-?kZ>(P^7^NG2<}CDMbSf`wvLXDCYK=tqtir9PfUPX08_QG zv60%GfLcJoe1kCl$tRznn54D4(+F10OQyjWT=lnrVM zRLKChUbql|7tPAb!cSr%WNIMl2h`^~at z%gEvdYuIRm(1B_AFVZF@C53x!e*E#rty{NJgB5JF!H1kQX_90g+iO9Zoi=S6$J#7e zvgFP94cdjcxHxKeCMG5Zp;p?e0Xxv3h?aclpWwBmBvSKACrd&{`si~=P z+YGVdXyEYxkVfP0Rsk{J$n`dd>F`|nVE^kTXLyGl7fN)BuKdr zhA)PP{2J4#p%$UF>S<|FNqcks>P6k7yeD$EHKNZ~Jf^|P(D_kA084FV&z>!e-bv| zefQmnhzPt^P*9NMBXJBnS=;e*E|`xe}~ewF+sK8Uk4Q4Wbs=uptKK_0XY1$+NZV*RKyAJUB5i z5%-+i$;(;8t2%I%v?KLx&EL3&fDodlo%Nv$L_bvbJ_}_p(@K{PlOs93AX!Y-}B! zHl;u8v^)qxwy&A{g9907B=dIq?(uf9vUFu$Y=$-)H*UlL`BGO`7dKiIJw3gvSFe&Q zfuW%xK0Y-B;4(Japd>}qqP7Sq5a!I8L&gRM29A!7WQ>^-5D-AdU8SU?1bLM_8LO$O zfpd%=J(>hJYinzK?2fD25I`^)$yf}s9f$Gx&9ky6XE1l7qRySa=;!5PzR4>(^2DA! zdx8&z=9j%*kpoS2)lO!{)4w*u{Cf4O8_2&C?;FB!AHeeE%eQaeP7QhJ>+55h zQbPb6Z2+_p-OC{a(;27o^72sNT3A>RM}fI?=~9#rEQ+`C@^TFg4NFT)_yn>m3e983 zj-lv6Z4D)G3d)fyeSCb#vn)xF^Ds~4KKD$B4R;S^C_bC`wb}RYM}!@_m2z|b^yzz# zo=He)f2dlXm;RlO)~4OzjO&ADW@hg0?$nS865*67Q{Xz}!JrUPZGLgH_c@#SC zRDtl#m~YS_!jYknq~It;7{j1!Fry(hLMUW_N1_NUEG%5PawVeQ=FOW$#rE^_3k?mW zMrYtRNRV=$dtN$w#A!dnUcK6a4BdG;r{Zp7e8|_;cGEAl{Pv94+R|K{mtm-_pPI{1 zoudI)P@5AcPM~hWeG{ARqS|<_H^(F(VAKi}$S!bh#^T$WqEN~6*c7X z=-stYGOk2obV>tyfW7TZ_W#$< zC-}Jdj{0s=RaJ#LO}JN&8xYeJ+%NF#Y0=TZUxFgU*M(VXgI@~|7caNFLrZ6fPTx#$%z`$X>Dq}eCGI=kN-1owHrMofW0=6 zk;=S%$uU8yv%e>6yAKmi4MP}Hv)$Ho-V!_FH!mx)Mh_W&F8TFN-ENYXm#3ztrmRP?3bJjLYH=c+Gtp@smK+GuHMDShwY<&(iy>$e;{uy5(I)qg)y=K4x?bv0rd$Lj*VzP>&_ zKGcxOjY~1AUkv+Vre5N0`h7eCOKs3DgoTAsLwQsdAm!6(|hUDhC8~tyvwOJw-aKWo!lN* z$oUczYZ_}SkA(zm_V90%`?WJ}sVU9(-{JoCf_a_?+P|2m5N&P$16PymKxc*oOaK4? 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+ 2u + 3v - w = 5
+ 3u + 4v + w = c:
+ +
+ +Answer + +c == 7 allows u = 1, v == 1, w == O. The column space is a plane. +
+ +2.What conditions on b1, b2, b3, b4 make each system solvable? Solve for x: + +![Question2](Images/lec8_q2.png) + +
+ +Answer + +Solvable if b2 = 2b1 and 3b1 - ,3b3 + b4 = O. Then X = +
+ +![Question2](Images/lec8_a1.png) + +
+(b) Solvable if b2 == 2b1 and 3b1 - 3b3 + b4 == O. Then x = +
+ +![Question2](Images/lec8_a2.png) +
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The column space is a plane. +c == 7 allows u = 1, v == 1, w == 0. The column space is a plane. 2.What conditions on b1, b2, b3, b4 make each system solvable? Solve for x: -![Question2](Images/lec8_q2.png) +![Question2](Images/lec8_q2.jpg)

Answer -Solvable if b2 = 2b1 and 3b1 - ,3b3 + b4 = O. Then X = +Solvable if b2 = 2b1 and 3b1 - ,3b3 + b4 = 0. Then X =
-![Question2](Images/lec8_a1.png) +![Question2](Images/lec8_a1.jpg)
-(b) Solvable if b2 == 2b1 and 3b1 - 3b3 + b4 == O. Then x = +(b) Solvable if b2 == 2b1 and 3b1 - 3b3 + b4 == 0. Then x =
-![Question2](Images/lec8_a2.png) +![Question2](Images/lec8_a2.jpg)
From 21086e5fdffcfc8c73d08db9a73ce5517cf91961 Mon Sep 17 00:00:00 2001 From: esha Date: Thu, 24 Feb 2022 02:39:18 +0530 Subject: [PATCH 3/3] lec8 modified --- Selected Questions/lec8.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Selected Questions/lec8.md b/Selected Questions/lec8.md index 468951c..04ea835 100644 --- a/Selected Questions/lec8.md +++ b/Selected Questions/lec8.md @@ -20,13 +20,13 @@ c == 7 allows u = 1, v == 1, w == 0. The column space is a plane. Answer -Solvable if b2 = 2b1 and 3b1 - ,3b3 + b4 = 0. Then X = +Solvable if b2 = 2b1 and 3b1 - 3b3 + b4 = 0. Then X =
![Question2](Images/lec8_a1.jpg)
-(b) Solvable if b2 == 2b1 and 3b1 - 3b3 + b4 == 0. Then x = +(b) Solvable if b2 = 2b1 and 3b1 - 3b3 + b4 = 0. Then x =
![Question2](Images/lec8_a2.jpg)