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
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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2b54370-3c39-40db-a25a-da953e4e00fe%2Fdcf9cf52-5e0d-4215-8bd7-f18a4ebf9928%2F8cops38_processed.png&w=3840&q=75)
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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