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. Miscellaneous. 2 O 0 (a) If A = 1 1 2 , nd all values of k such that A is invertible. 1 k k2 (b) If A is 3 X 3 matrix such that: 1 2 . A 1 = 2 , 1 2 1 7 o A O = O , 7 49 o and rankA =2, what is the characteristic polynomial of A? Explain! (c) If A is an arbitrary 3 X 3 matrix with eigenvalues 1, 2,3, must A be invertible? Explain. (d) Suppose A is an arbitrary matrix with eigenvalue A and corresponding eigenvector v. Determine if v is an eigenvector of A'l, A2, and A + 2I. If so, give the corresponding eigenvalues