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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. 02 AS A= 41

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. 02 AS A= 41

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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 0 2 -1 -2 2 -3 02 A5: A = = , A5 000 000 Are the two matrices similar? If so, find a matrix P such that B = P-¹AP. (If not possible, enter IMPOSSIBLE.) 200 100 03 0 0 1 0 003 002 A = B =
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. -3 0 2 -1 -2 2 -3 02 A5: A = = , A5 000 000 Are the two matrices similar? If so, find a matrix P such that B = P-¹AP. (If not possible, enter IMPOSSIBLE.) 200 100 03 0 0 1 0 003 002 A = B =
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