3. (15%) Assume A E R4X4 has eigenvalues 1, 2, 3, 4. Find (52 + (A - 51) 999 where | o | denotes determinant. (Hint: Note A has distinct eigenvalues and can be put into an eigendecomposed form A = VAV- such that [A - 51| = [VAV-1 -5VIV-1.) 4. (a) (10%) Assume matrix A has two distinct eigenvalues 1 and 12, their corresponding eigenvectors are v1 and v2, respectively. Show v1 + 12 is not an eigenvector of A. (b) (5%) If A E Rnxn is invertible and diagonalizable, prove that A- is also diagonalizable