Consider the following. -10 36 A = P = -1 -3 11 (a) Verify that A is diagonalizable by computing P-1AP. 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 × n matrices, then they have the same eigenvalues. (11, 12) =

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.4: Similarity And Diagonalization
Problem 7EQ
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Consider the following.
-10 36
-3 -4
A =
P =
-3 11
-1 -1
(a) Verify that A is diagonalizable by computing P-lAP.
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.
(11, 12) =
Transcribed Image Text:Consider the following. -10 36 -3 -4 A = P = -3 11 -1 -1 (a) Verify that A is diagonalizable by computing P-lAP. 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. (11, 12) =
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