25. In each case find the characteristic polynomial, eigenvalues, eigenvectors, and (if possible) an invertible matrix P
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25. In each case find the characteristic polynomial, eigenvalues, eigenvectors, and (if possible) an invertible matrix P
25. In each case find the characteristic polynomial, eigenvalues, eigenvectors, and (if possible) an invertible matrix P such that P-AP is diagonal. (a) A= [1 2 (3 21 (b) A = [² TO 1 07 (c) A = 3 0 1 1200 [2 1 1 (d) A = 10 1 0 11-12 11 -2 3 e) A = 2 6 -6 1 2 26. In each case find the A" using the Diagonalization concept, and hence find A10 (a) A= ( 11 [1 2] (6) A= ( 32 A A=11
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