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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Linear Algebra #2
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.
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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