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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-lAP 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. -10 -18 A = 6 11

Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = P-lAP 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. -10 -18 A = 6 11

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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-lAP 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. -10 -18 A = 6 11
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-lAP 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. -10 -18 A = 6 11
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