1.ear, 1 = 10/2, vs a is o an. = (to], 202, toy} a basis of W. The matrix representation of T with respect of 3 1 0 the bases St and S2 is 0 2 5 . [ ] 0 0 7
(a) Find T (vs) (b) Find T (vi — 2v2 5v3) (c) Find v E V such that T(v) = ws 2. Let S = {vi, v2, vs} be a basis of V and let 2' :V —. V be the linear map defined by Tvi = v2, Tut = vs, and Tvs = vt. Find the matrix representation of T with respect to S. 3. The matrix representation of T : Rs —. Rs with respect to the basS 1 0 1 S= ((1,0,0) ,(1,1,0) ,(1,1,1)) is 0 1 1 . 0 0 1
(a) Find v E RS such that Tv = ( ,1,1) (b) Find the matrix representation of 2' with respect to the canonical basis of Rs.
4. Find a linear map T : Rs —¦ le such that Null (T) = span {(1,0,1) , (0, 1, 1)} Range (T) = span {(0,1,0)} and find the matrix representation of T with respect to the canonical bas of Rs. 5. The matrix representation of T : Rs —. Rs with respect to the basS 1 1 1 S = (0,1,1) , (0, 1, 1) , (0, 0,1)} is 0 1 4 . Find bases of Null (T) [ 0 0 0 and Rangc(2'). [ 6. Let A = 11 2] and define T : if2x2 —, M2x2 bY T(B) = AB — BA. — 0 Find the matrix representation of T with respect to the canonical basis of Ma x2.