2. Let A = = 1 -4 -2 (a) Compute the eigenvalues of A. (b) Find a basis for each eigenspace of A. (c) Use the Diagonalization Theorem to find an invertible matrix P and a diagonal matrix D so that P-¹AP = D.
2. Let A = = 1 -4 -2 (a) Compute the eigenvalues of A. (b) Find a basis for each eigenspace of A. (c) Use the Diagonalization Theorem to find an invertible matrix P and a diagonal matrix D so that P-¹AP = D.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 79E
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Question
![2.
Let A =
=
1 -4
-2
(a) Compute the eigenvalues of A.
(b) Find a basis for each eigenspace of A.
(c) Use the Diagonalization Theorem to find an invertible matrix P
and a diagonal matrix D so that P-¹AP = D.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d410cd6-8fc6-4d13-8ff0-7a43ba3056bc%2F4dfab7c0-446b-4d76-af15-2aea1b94937f%2Fokngw3l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.
Let A =
=
1 -4
-2
(a) Compute the eigenvalues of A.
(b) Find a basis for each eigenspace of A.
(c) Use the Diagonalization Theorem to find an invertible matrix P
and a diagonal matrix D so that P-¹AP = D.
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