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)...

1 answer below »
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.

Answered Same DayDec 22, 2021

Answer To: 1.ear, 1 = 10/2, vs a is o an. = (to], 202, toy} a basis of W. The matrix representation of T with...

Robert answered on Dec 22 2021
127 Votes
Hints for questions: Answer already provided
3 As I already discussed in the previous clarification
, We know that column
of matrix is given by image of basis element. That is why we have
T (1, 0, 0) = (1, 0, 0)
How we conclude above line??
We have given first element of basis is (1, 0, 0) and first column is (1, 0, 0).
Hence we have have by definition of matrix...
SOLUTION.PDF

Answer To This Question Is Available To Download

Related Questions & Answers

More Questions »

Submit New Assignment

Copy and Paste Your Assignment Here