Question

Previous Problem Problem List Next Problem (1 point) Let 07 A = -5 6 6 and b -3 3 -2 L 9 -437 96 R4 by T) = AE. Find a vector ã whose image under T is . Define the linear transformation T: R3 Is the vector i unique? choose Note: In order to get credit for this problem all answers must be correct

Answer 1

Given: A and 5 اللي ما عاد 2 6 3 -3 -5 6 i - 2 7 43 Let i= such that Au=5 R, LR The augmented matrix is [A 5 = 4 a-51411 7-5 6 61-67 I 1-3 3 -2 -11 19-43 7196 1-5 6 R₂ R₂ + 521 RzR3 +3R RG RG 9R, w a na - 0 - juta picha nje planet 0 n5 ed aló A toh abala - when we watu wu na waten we na atakan anak 0 policia puhe 0 - -o o o R₂ ₃ 2 2 2 2 R, R, - 12 R RzRy - 3 / 3 ₂ Ruhut 95 R -2865 - - o Rzx - 34 h 00 -oo- - ut on na suchou - 6 R, R₂ R, + 21 R3 h + 1 R3 0 1 0 0 0 1 1 0 0 0 0 1,= 5, ų=-2, 1₂=-5 R4-R3
I'll
• Here, rank of the coefficient matrix=3 By rank-millity theorem. rank (A) + hallity (A) = dimension of R² 3thullity (A)=3 nullity (A) = 0, ie dimension of Kerlte ..ker (T) = {0} {A linear transformation » T is one-to-one T is one-to-one, if Kerly) = {0} : vector ñ is unique.