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Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = P-1AP is the diagonal form of A. Prove that AK = PBKP-1, where k is a positive integer. Use the result above to find the indicated power of A. -3 02 -1 -2 2 A5 -3 02 A5 = A = 000 000 →

Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = P-1AP is the diagonal form of A. Prove that AK = PBKP-1, where k is a positive integer. Use the result above to find the indicated power of A. -3 02 -1 -2 2 A5 -3 02 A5 = A = 000 000 →

Elementary Linear Algebra (MindTap Course List)
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Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = P-1AP is the diagonal form of A. Prove that AK = PBKP-1, where k is a positive integer. Use the result above to find the indicated power of A. +6 A = -1 -2 2 A5 A5 = -3 02 -3 02 I
Transcribed Image Text:Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = P-1AP is the diagonal form of A. Prove that AK = PBKP-1, where k is a positive integer. Use the result above to find the indicated power of A. +6 A = -1 -2 2 A5 A5 = -3 02 -3 02 I
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