Question 2. (a) Give a real matrix A with characteristic polynomial -(t - 2)?(t - 3) such that A is NOT diagonalizable or show that no such matrix exists. (b) Give real matrix B with characteristic polynomial -(t -2) (t -3) (t -4) such that B is NOT diagonalizable or show that no such matrix exists. (c) Give a real matrix E with characteristic polynomial -(t - i) (t -3) (t -4) such that E IS diagonalizable (over the complex numbers) or show that no such matrix exists. (d) Give a real, symmetric matrix F with characteristic polynomial -(t - i) (t + i) (t -4) such that F IS diagonalizable (over the complex numbers) or show that no such matrix exists