Find the eigenvalues A₁ < A₂ < A3 and associated unit eigenvectors ₁, 2, 3 of the symmetric matrix 4 -2 -2 0 2 2 0 The eigenvalue X₁ The eigenvalue X₂ The eigenvalue X3 = -2 = 0 = 6 A = -2 -2 [ has associated unit eigenvector ū₁ = has associated unit eigenvector ū₂ = has associated unit eigenvector ū3 = | 0 -1 1 1 1 1 -2 1 1

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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Find the eigenvalues X₁ < λ2 < A3 and associated unit eigenvectors ū1, ū2, ū3 of the symmetric matrix
4
-2 -2
O
2
2
0
The eigenvalue X₁ -2
The eigenvalue X₂
=
=
O
The eigenvalue X3 6
=
A =
-2
-2
has associated unit eigenvector ₁
=
has associated unit eigenvector 2
=
has associated unit eigenvector ū3
=
L
0
-1
1
1
1
1
-2
1
1
Transcribed Image Text:Find the eigenvalues X₁ < λ2 < A3 and associated unit eigenvectors ū1, ū2, ū3 of the symmetric matrix 4 -2 -2 O 2 2 0 The eigenvalue X₁ -2 The eigenvalue X₂ = = O The eigenvalue X3 6 = A = -2 -2 has associated unit eigenvector ₁ = has associated unit eigenvector 2 = has associated unit eigenvector ū3 = L 0 -1 1 1 1 1 -2 1 1
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