Question
(1 point) Let 6 -5 5 16 47 5 4 6 A= and b= 3 3...
(1 point) Let 6 -5 5 16 47 5 4 6 A= and b= 3 3 11 -4 -3 -8 116 40 Define the transformation T:R? R4 by T(2) = Ax. Find a vector x whose image under T is b. = Is the vector x unique? unique
Answers
If rank of matrix is = rank of augmented matrix = number of variables. Then system has unique solution.
Given A = 6 - 5 5 6. 5 3 3 40 -4 -3 ah 16 47 Also - 8 116 T(2) T(x) = Aa f b So Construct Al = b Augmented matrix & find Rank by reducing it form. of matrix A Echleon -5 4 5 6 3 3 16. 47 -8 : 116 11 40 -3 RA → R-R2 1 -1 -31 4 3 47 3 - 8 40 -3 . 116 Rg → Rg -5R, R₂ R₂ - 3R, Ry Ry - 111 . -31 1 202 49 30 139 85 457 0 : R₂ 49 R - 30R2 Ry 4984 - 139 R₂ -1 49 . o o o Р - 31 202 -1895 -5685 . оо -379 - 1137 . 379 Ry 1137 R 1 -9 -31 0 49 202 - 1895 O 0 -379 . O 0 O So = 3 2 Rank (A) Rank (A:B) = 3 Number of variables So system has unique solution. = 3 -1 O 49 of 11 31 209 - 1895 -379 z Oo 0 0 x-gy-z -2 = - 31 494 +112 = 202 -3792= a 1895(2 = 5 че + 17 Әo2 + 55 = 209 Эo2 — 55 14 Кон hon % = 3 у — bo- - Z – 3| С – 91 - 5 = - 31 - - 3) +32 L=11 So 1 3 yes у СА unique.
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