Find the eigenvalues 11 <12 and associated unit eigenvectors 1, 2 of the symmetric matrix 8 -6 A = -6 -8 The smaller eigenvalue ₁ = has associated unit eigenvector u₁ = The larger eigenvalue 12 = has associated unit eigenvector 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 11 <12 and associated unit eigenvectors 1, 2 of the symmetric matrix
8
-6
A =
-6
-8
The smaller eigenvalue ₁ =
has associated unit eigenvector u₁
=
The larger eigenvalue 12 =
has associated unit eigenvector ₂ =
Note: The eigenvectors above form an orthonormal eigenbasis for A.
Transcribed Image Text:Find the eigenvalues 11 <12 and associated unit eigenvectors 1, 2 of the symmetric matrix 8 -6 A = -6 -8 The smaller eigenvalue ₁ = has associated unit eigenvector u₁ = The larger eigenvalue 12 = has associated unit eigenvector ₂ = Note: The eigenvectors above form an orthonormal eigenbasis for A.
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