# Linear Transformation

1. Nov 17, 2008

### Maxwhale

1. The problem statement, all variables and given/known data

T: R3 --> R2 by T(x,y,z) = (z-x , 2y -x)
v = (2, -1, -3)
B = {(0,0,1),(0,1,1),(1,1,1,)}
C = {(1,-1), (2,1)}

What is [T]BC
what is [v]B
and what is T(v)

2. Relevant equations

No clue

3. The attempt at a solution

I found out [T]B and that's where i am stuck.

2. Nov 17, 2008

### Staff: Mentor

I'm pretty sure that $$[T]_{BC}$$ is the matrix representation of T on the vectors in B, in terms of the basis vectors in C.

For example, T(b1) = T(0,0,1) = (1,0)
In terms of the basis in C, this is 1/3 (1, -1) + 1(2,1)

So the first column of $$[T]_{BC}$$ is (1/3, 1) (written as a column vector).
You need to do this for the other two vectors in B.

$$v_B$$ is the representation of v in terms of the basis B.
T(v) is pretty straightforward.