Linear transformation - adding and subtracting?

[Niles]

[SOLVED] Linear transformation - adding and subtracting?

Homework Statement

Suppose T : P2 -> P2 is a linear transformation satisfying T(3 − x + 4x^2) = 1 + x − x^2 and
T(2 − 3x + 2x^2) = 7 + 3x + 2x^2.
Find T(7x + 2x^2).

The Attempt at a Solution

First of all, it's linear. To find T(2x^2), I can say -x^2-2x^2 = -3x^2 = T(2x^2)? And similarily for T(7x)?

 

[Niles]

No wait, I solved it.. I can't do what I did in my original post.

I have to solve a linear system of equations to find T(7x + 2x^2) written from T(3 − x + 4x^2) and T(2 − 3x + 2x^2).

Bottom line is, I solved it.