Problem 4. a. Let U : P3(R) - P2(R) and T : P2(R) - P3(R) be the linear transformations defined by U(f ( x)) = 3f' (x) and T(f(x)) = 6 0 f(1)dt. respectively. Let B = { 1, x, x } and y = {1, x, x2, x } be the standard ordered bases for P2(R) and P3 ( R), respectively. Compute the representation matrix for their composition [UTI. b. Let I be a vector space and let T : V - V, U1 : V - V and U2 : V - V be linear transformations. Prove that T(U1 + U2) = TU1 + TU2