Linear

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...
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3. Linear

Consider the following.
-5
1 0
0 1 -3
A =
0 -1 0 I, P =
0 4
1 2
4 -2 1
2
(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.
(A1, 12,
(4, dz, dz) = (
Transcribed Image Text:Consider the following. -5 1 0 0 1 -3 A = 0 -1 0 I, P = 0 4 1 2 4 -2 1 2 (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. (A1, 12, (4, dz, dz) = (
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