Consider the linear mapping $T:P2(R) → P2(R)$ given by,
$T p(x) = (1−x^2)p′′(x)−2xp′(x)$
Let $B1$ = {$1+x,1+x^2,1+x+x^2$} ⊂ $P2(R)$. Then $B1$ is a basis for $P2(R)$
(a) Compute the matrix $M(T,B1,B1)$.
(b) Let $p(x) = 1+2x−3x^2.$ Compute
(i) $[p]B1$
(ii) $[Tp]B1$
(iii) $M(T,B1,B1)[p]B1$
For part a) i got
$(0 6 6
2 2 4
-2 -6 -8)$
But i dont know if its correct and i am very confused for part b) im struggling to see what its asking me to compute.