# Math Help - [SOLVED] Matrix of a lin. transform

1. ## [SOLVED] Matrix of a lin. transform

Let $T : P_2(R) \to P_2(R)$ be the linear transform defined by $T(f)=2f'' +3f'-f$.

Let E and F be to bases: $E=\{1, x, x^2\}, ~F=\{1+x,1+x+x^2,1-2x+x^2\}$.

Determine the matrix representation, C, of T relative to E.
-----

My approach (don't know if it's correct):

Let f = $ax^2+bx+c \in P_2$.

$f' = 2ax + b, ~ f'' = 2a$

$\therefore T(f) = (-a)x^2+(6a-b)x+(4a+3b-c)$

$\therefore C = \begin{bmatrix}-1&0&0\\6&-1&0\\4&3&-1\end{bmatrix}$

which is sorta correct, except: The coords of $f$ relative to E are (c,b,a) not (a,b,c)! So if I'm given a vector X relative to E, CX won't be correct.

What should I have done?

2. ah, nevermind, I realised C should be:

$C = \begin{bmatrix}-1&3&4\\0&-1&6\\0&0&-1\end{bmatrix}$

since $T(c,b,a)=(-c + 3b + 4a, -b + 6a, -a)$