3. Determine whether each of the following transformations is a linear transformation T : P1 - P1. For those that are, give their matrix [T] B, B relative to the standard basis B = {1, x}. (a) T(ao + alx) = (3ao + a1) + (ao - 201)x. (b) T(ao + alx) = (ao - 501) + (aoal)x. (c) T(ao + alx) = (ao, a1). 4. Let T : P2 - P3 be the transformation defined by T(p) [x] = xp(x - 3). Let B be the standard basis for P2 and let B' be the standard basis for P3. (a) Find [T] B' , B. (b) Let p(ac) = 1 + x - x2. Use [T] B', B to find T(p). N 0 3 1 5. Show that v = (1, 0, -1, 0) is an eigenvector of A = A CO - , and find the corresponding eigenvalue. NN 6. Let a be a nonzero vector in R", and let P = lla |/2 aa . Show that 1 is an eigenvalue of P