Question

(1 point) Let 1-11 ſi -1 31 A = 0 1 -1 and b=1-2 L-1 -2 0 [7] Define the linear transformation T:R* R* by T(T) = A. Find a vector a whose image under T is b. Is the vector i unique? choose choose unique Note: In order to get cred not unique all answers must be correct

Answer 1

Let z = [1] EIR? such that T (2) = 5 > AR = 47370 W. TA 10 -2 0 || 2 1 7 so the augmentedi matrix ist 1-1 3-17 ri - 3- o s To1-7- 2ar To 1 -2 hhth 14 -2 0 7 10-3 3 6 eě n II 02 -3 o1 -1 -2] RiR, AR2 lo O O O Rz7R3+3R, So, the system reduces to x +22= -3 928 2029.) (e-)2 = Y - Z = -2. Let z=1, then x=-3-22 = -3-22 -5 and y=-2+2=-2+13-1 so - x = is a vector such IT- that T(2)=5 . - Now, if za t, then x=3-22=-3+2=-1 - and y=-2+2 =-2-1=-3.

Then ² = -3 is another rector such So, that T(*)=b . ² is not unique.