Problem 2. TRUE/FALSE. (3 points each) Be sure to clearly state whether the items below are true or false. Then you must fully justify your answer: if true, give a brief explanation (e.g. cite a relevant theorem from the book or class notes, or show the necessary calculations); if false, supply a counterexample. (a) If an n x n matrix A is diagonalizable, then so is A'. (b) If v is an eigenvector of an n x n matrix A with corresponding eigenvalue ), then v is also an eigenvector of the matrix A - aln, for every de R. (c) Given a vector space V, the change of coordinates matrix [Iv] from #' to 8 is always diagonal- izable. (d) The linear operator 7 : R3 -> R3 that reflects a point (r, y, z) across the plane ar + by +c= =0 (a,b,ce R) is diagonalizable