Find the eigenvalues A₁ < A2 and associated unit eigenvectors 1, 2 of the symmetric matrix -1 A = 43 -81 8 11 The smaller eigenvalue A₁ = -5 has associated unit eigenvector i 1 2 The larger eigenvalue 2 = 15 has associated unit eigenvector 2 = 1 1 2 Note: The eigenvectors above form an orthonormal eigenbasis for A.

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 A₁ < A2 and associated unit eigenvectors 1, 2 of the symmetric
matrix
-1
A =
43
-81
8
11
The smaller eigenvalue A₁ = -5
has associated unit eigenvector i
1
2
The larger eigenvalue 2 = 15
has associated unit eigenvector 2 =
1
1
2
Note: The eigenvectors above form an orthonormal eigenbasis for A.
Transcribed Image Text:Find the eigenvalues A₁ < A2 and associated unit eigenvectors 1, 2 of the symmetric matrix -1 A = 43 -81 8 11 The smaller eigenvalue A₁ = -5 has associated unit eigenvector i 1 2 The larger eigenvalue 2 = 15 has associated unit eigenvector 2 = 1 1 2 Note: The eigenvectors above form an orthonormal eigenbasis for A.
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