Consider the following. -6 12 -3 -4 P = 1 A = -1 -1 -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. (11, A2) =
Consider the following. -6 12 -3 -4 P = 1 A = -1 -1 -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. (11, A2) =
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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Transcribed Image Text:Consider the following.
-6 12
-3 -4
A =
P =
-1
1
-1 -1
(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 x n matrices, then they have the same eigenvalues.
(11, 12) :
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