The matrix The eigenvalue X₁ is -2 A = The eigenvalue X2 is 0 ГО 0 0 has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis for each eigenspace. 0 -2 01 0 2 0 and a basis for its associated eigenspace is and a basis for its associated eigenspace is { 0 -2 2 0 -2 2 1 0 0

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 24EQ
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The matrix
The eige alue X₁ is -2
ΓΟ
A 0
-
The eigenvalue X2 is 0
has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis for each eigenspace.
0 01
429
-2 0
0 2 0
and a basis for its associated eigenspace is
and a basis for its associated eigenspace is
0
Ņ
2
0
-2
2
1
0
0
Transcribed Image Text:The matrix The eige alue X₁ is -2 ΓΟ A 0 - The eigenvalue X2 is 0 has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis for each eigenspace. 0 01 429 -2 0 0 2 0 and a basis for its associated eigenspace is and a basis for its associated eigenspace is 0 Ņ 2 0 -2 2 1 0 0
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