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Consider the following. -7 24 3 -4 A = P = -1 (a) Verify that A is diagonalizable by computing P-AP. p-'AP = (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (1,, A2) :

Consider the following. -7 24 3 -4 A = P = -1 (a) Verify that A is diagonalizable by computing P-AP. p-'AP = (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (1,, A2) :

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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PLEASE, answer the following 2 problems, thanks.

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 -6 -11 Ak = PBkp-1, where k is a positive integer. Use the result above to find the indicated power of A. 10 A = 18 AS -1/3 1 AS = 1 1
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 -6 -11 Ak = PBkp-1, where k is a positive integer. Use the result above to find the indicated power of A. 10 A = 18 AS -1/3 1 AS = 1 1
Consider the following. -7 24 -3 -4 A = P = -1 -1 (a) Verify that A is diagonalizable by computing P-AP. p-1AP = (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (1, 12) = (
Transcribed Image Text:Consider the following. -7 24 -3 -4 A = P = -1 -1 (a) Verify that A is diagonalizable by computing P-AP. p-1AP = (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (1, 12) = (
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