# Linear transformation of matrices

1. Oct 18, 2009

### geft

Sorry for the poor formatting, I keep getting errors with Latex in preview. I'll appreciate anyone who could reformat the question into Latex.

Let T: R3 -> R2 be defined by T(x, y, z)T = (x +z, y - z)T. Find the matrix of T with respect to the bases B = {(1,1,0)T,(0,1,1)T,(1,0,1)T} and B' = {(1,1)T,(-1,1)T}.

Here is what I've done. I don't know what's wrong and I'm going crazy because I can't find what's wrong with it. I believe it's my careless mistake, but I've been checking again and again to no avail.

T(1,0,0)T = (1, 0)T
T(0,1,0)T = (0, 1)T
T(0,0,1)T = (0, -1)T

AT = (1 0 0, 0 1 -1)T
PB = (1 0 1, 1 1 0, 0 1 1)T
PB' = (1 -1, 1 1)T

PB'-1 = 1/2 (1 1, -1 1)T

PB'-1ATPB = (1 0 0, 0 0 -1)

T(u1) = T(1,1,0)T = (1, 1)T $$\neq$$ v1 + 0v2
T(u2) = T(0,1,1)T = (1, 0)T $$\neq$$ 0v1 + 0v2
T(u3) = T(1,0,1)T = (2, -1)T $$\neq$$ 0v1 + -v2

Last edited: Oct 18, 2009