1. ## Matrix Representation

Find a matrix representation for the "even part" linear transformation P: R<=3[x] --> R <=3[x]

Note: R<=3[x] is the set of all polynomials with degree 3 or less

given by (Pf)(x) = [ f(x) + f(-x) ] / 2,

with respect to the basis {x^3, x^2, x^1, x}. Use this to give a formula for P(ax^3 + bx^2 + cx + d).

2. ## Re: Matrix Representation

$\begin{bmatrix}0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$
P(...) = bx^2 + d