SF56. (a) Show that the set of polynomials $B = \{p_1, p_2, p_3\}$, defined by
$p_1(x) = x^2 + 1$, $p_2(x) = 2x^2 + x - 1$, $p_3(x) = x^2 + x$
forms a basis for $P_2$.
(b) Find the unique representation of the polynomial $x + 1$ in terms of this basis.
That is, find $a$, $b$, $c$ so that $\begin{bmatrix} a \\ b \\ c \end{bmatrix} = x + 1$, or $rep_B(x + 1) = \begin{bmatrix} a \\ b \\ c \end{bmatrix}$.