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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-'AP is the diagonal form of A. Prove that Ak = PBKP-1, where k is a positive integer. %3D Use the result above to find the indicated power of A. 20 -2 A = 0 2 -2 3 0 -3 A5 =

Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = P-'AP is the diagonal form of A. Prove that Ak = PBKP-1, where k is a positive integer. %3D Use the result above to find the indicated power of A. 20 -2 A = 0 2 -2 3 0 -3 A5 =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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-'AP is the diagonal form of A. Prove that Ak = PBKP-1, where k is a positive integer. %3D Use the result above to find the indicated power of A. 20 -2 A = 0 2 -2 3 0 -3 A5 =
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-'AP is the diagonal form of A. Prove that Ak = PBKP-1, where k is a positive integer. %3D Use the result above to find the indicated power of A. 20 -2 A = 0 2 -2 3 0 -3 A5 =
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