dp(x) Let T : P2 → P3 be the linear transformation given by T(p(x)) – xp(x) + x²p(x) dx where p2, P3 are the spaces of polynomial of degree at most 2 and 3 respectively. (a) Find the matrix...

Need help with B and C

Extracted text: dp(x) Let T : P2 → P3 be the linear transformation given by T(p(x)) – xp(x) + x²p(x) dx where p2, P3 are the spaces of polynomial of degree at most 2 and 3 respectively. (a) Find the matrix representation of T relative to the bases {1, x, x²} and {1, x, x², x³} for P2 and p3. (b) Find the kernel of T. (c) Find a basis for the range of T.