Linear transformation matrix?

Question

T:R2-->R2 is defined as T:(x,y)= (x+y,x-y)..
Using the bases B1=B2= {(1,-1), (-3,2)} find the transformation matrix.

please elaborate..the answer is listed as

-6 17
-2 6

Answer 1

you need to do the following:
T( (1,-1))= (0, 2) = -6 (1,-1) - 2 (-3,2) so the first column of your matrix is:
-6
-2

now
T ( (-3,2) ) = ( -1, -5) = 17 (1,-1) + 6 (-3,2), so the second column of your matrix is:
17
6

when you put them together you get:
-6 17
-2 6
'

Answer 2

The matrix A is 4x6. The transformation makes use of matrix multiplication to coach a vector x with 4 components right into a vector with 6. The area is R^4 and the codomain R^6. As for b. i do no longer recognize what it capacity by a picture so i won't be able to help out.

Answer 3

T is

1 1
1 -1

relative to {e1,e2}

express new basis vectors

1 -1 | 1 0 | = 1 -1
-3 2 | 0 1 | = -3 2

Won't finish, but the idea is that v in basis b1 is expressed as lkin comb of e1,e2. Then apply T and absorb the constants into new matrix elements so that you're left with coeffieciets of v w.r.t. the new basis.

I'm going to go ahead and post this although I don't much care for it.