Find the eigenvalues A1 < dg and associated unit eigenvectors ū1, ūz of the symmetric matrix 12 A = 6- -9 -12 The smaller eigenvalue A1 = -15 has associated unit eigenvector ủ1 = The larger eigenvalue A2 15 A has associated unit eigenvector ủ2 = 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 ū1, ūz of the symmetric matrix
[12
A
6-
-12
The smaller eigenvalue A1
= -15
2 has associated unit eigenvector ū1 =
The larger eigenvalue X2 = 15
has associated unit eigenvector ü2 =
Note: The eigenvectors above form an orthonormal eigenbasis for A.
Transcribed Image Text:Find the eigenvalues A1 < A2 and associated unit eigenvectors ū1, ūz of the symmetric matrix [12 A 6- -12 The smaller eigenvalue A1 = -15 2 has associated unit eigenvector ū1 = The larger eigenvalue X2 = 15 has associated unit eigenvector ü2 = Note: The eigenvectors above form an orthonormal eigenbasis for A.
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