1. (1 point) Let A = -9 -8 a) Is matrix A diagonalizable? |? (incorrect) 4. (1 point) Let A be a 3 x 3 diagonalizable matrix whose b) If A is diagonalizable, find a matrix P along with its in- eigenvalues are 21 =4, X2 = -1, and 23 = -2 with correspond- verse and a diagonal matrix D such that A = PDP-1 ing eigenvectors vi = If A is not diagonalizable, enter 0 in each of the entries be- low. respectively. Express A as PDP- where D is a diagonal matrix and use this to find AS. Answer(s) submitted: -EEE] Answer(s) submitted: incorrect) 1 2. (1 point) LetA = -6 -3 6 -2 a) Is matrix A diagonalizable? |? b) If A is diagonalizable, find an invertible matrix P and di- agonal matrix D such that PAP = D. Leave all entries in the (incorrect) matrices below as exact values. 5. (1 point) If A is not diagonalizable, enter 0 in each of the entries be- Suppose that A, P, and D are n x n matrices. low. Check ALL true statements given below: 0 and D = 0 . A. If A is diagonalizable, then A is invertible. . B. A is diagonalizable if A = PDP- for some diagonal Answer(s) submitted: matrix D and some invertible matrix P. . C. A is diagonalizable if and only if A has n eigenvalues, counting multiplicities. (incorrect) . D. If there exists a basis for IR" consisting entirely of eigenvectors of A, then A is diagonalizable. 3. (1 point Answer(s) submitted: Given that the matrix A has eigenvalues A1 = -3 with corre- sponding eigenvector vi = and 22 = 3 with corresponding (incorrect) 6. (1 point) Suppose that A, P, and D are n x n matrices. A = = = Check the true statements below: Answer(s) submitted: . A. If A is invertible, then A is diagonalizable. . B. If A is diagonalizable, then A has n distinct eigenval- ues. . C. A is diagonalizable if A has n distinct eigenvectors. Q.E.D. . D. If AP = PD, with D diagonal and P invertible, then the nonzero columns of P must be eigenvectors of A. Answer(s) submitted: (incorrect) A. det (P-'AP)