Please answer parts a, b, and c. Note from the professor was, "pay attention in question 7 to when your answers should be columns in R4 and when they should be polynomials in P3".

7. Let V again be 733 = {am3+bm2+cm+d : a, b, c, d E R}. Let T: V > V be the linear map sending f($) to the polynomial m - f'(3; 2). (a) Find the matrix representation of T with respect to the ordered basis {1, 3:, $2, $3}. (b) Find the eigenvalues of the transformation T. For each eigenvalue A, nd an eigenvector for A in 733. (c) (EXTRA CREDIT) Repeat this problem except let T be the map f(sc) I> m - f' (:1: q) for an unknown q; some of your answers will still have a q in them, and the answers one would get in easy mode should be what you would get if you plug in q = 2