[SOLVED] Linear Transformations (polynomials/matrices)

jesuslovesu

Never mind, I can see it now, thanks

1. The problem statement, all variables and given/known data
Let S be the linear transformation on P2 into P3 over R. S(p(x)) = xp(x)
Let T be the linear transformation on P3 over R into R2x2 defined by T(a0 + a1x + a2x^2 + a3x^3) = [ a0 a1; a2 a3]

Find a formula for TS(p(x)).

3. The attempt at a solution
The first thing I do is find the S(A) where A is the standard basis of P2 and I place that into a transition matrix from the basis B (std. basis of P3).
[S]B,A = [0,0,0;1,0,0;0,1,0;0,0,1]
Then I do the similar steps for fining [T]C,B where C = E2x2
[T]C,B = I4 (identity matrix of a 4x4)
Multiplying the matrix yields: [T]*[S] = [0,0,0;1,0,0;0,1,0;0,0,1]

I am fairly positive that the math up to this point is accurate. (I get the correct range of T).

My question is how do I specifically find the formula for TS(p(x)) using the last matrix that I found? I know it's a mapping of P2 into R2x2, but I don't quite see how they get [0, a0; a1, a2] as the matrix. I know it lines up with TS, but still