Question regard writing linear transformation into matrix

Hey guy, I have some problem regard to linear transformation, I can conver something like this $\displaystyle T(x, y, z)=(x+ 2*y -z, x-y+2z,-y+z)$ into matrix form but I don't know how to convert "the following" into matrix form. Can you guy give me advice about how to do it?

Let $\displaystyle T : P3 --> P3 $be the linear transformation deﬁned by

$\displaystyle T(p(x)) = p(x+ 1) +p(2-x)$

(For example, $\displaystyle T(x^2 + 7) = (x+ 1)^2 + 7 + (2-x)^2 +7=2x^2-4x+ 18.)$

Find the matrix of T with respect to the standard basis $\displaystyle B = {1, x, x^2, x^3}$ for P3.

best regard

Junks

Re: Question regard writing linear transformation into matrix

Start by writing out explicitly the value of T on an arbitrary cubic polynomial ax³ + bx² + cx + d.