Find the eigenvalues X₁ < ₂ and associated unit eigenvectors 1, 2 of the symmetric matrix [19 12 12 1 The smaller eigenvalue X₁ = -5 The larger eigenvalue X2 25 A = has associated unit eigenvector ū₁ = has associated unit eigenvector ū₂ = Note: The eigenvectors above form an orthonormal eigenbasis for A. - -15 25 25 15

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 41EQ
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Find the eigenvalues λ₁ < λ2 and associated unit eigenvectors 1, ủ2 of the symmetric matrix
[19 12]
12 1
The smaller eigenvalue X₁ =
=
The larger eigenvalue X2
-5
= 25
A
=
has associated unit eigenvector ₁
=
Note: The eigenvectors above form an orthonormal eigenbasis for A.
has associated unit eigenvector 2
-
-15
25
25
15
Transcribed Image Text:Find the eigenvalues λ₁ < λ2 and associated unit eigenvectors 1, ủ2 of the symmetric matrix [19 12] 12 1 The smaller eigenvalue X₁ = = The larger eigenvalue X2 -5 = 25 A = has associated unit eigenvector ₁ = Note: The eigenvectors above form an orthonormal eigenbasis for A. has associated unit eigenvector 2 - -15 25 25 15
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