Using the standard basis S = {r4, t3, t3, t2, t, l} for P4, deter-mine a matrix representing the transformation from P. to P4 given in each of Problems. Then apply your matrix to the following polynomials:
(a) g(t) = t4 - t3 + t2 - t + 1
(b) q(t) = t4 + 2t2 + 4
(c) r(t) = -4t4 + 3t3
(d) w(t) = t4 - 8t2 + 16