Find the eigenvalues λ₁ < ^₂ < 3 and associated unit eigenvectors ₁, 2, 3 of the symmetric matrix 0 0 4 A = 0 -2 0 4 0 0 The eigenvalue λ₁ = has associated unit eigenvector ₁ = The eigenvalue ₂ has associated unit eigenvector ₂ =

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
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Find the eigenvalues λ₁ < λ₂ < λ3 and associated unit eigenvectors ₁, 2, 3 of the symmetric matrix
0
0 4
^-|
0-2
4 00
The eigenvalue ₁ =
has associated unit eigenvector ₁
=
The eigenvalue 1₂
has associated unit eigenvector ₂
=
The eigenvalue 13
has associated unit eigenvector uz
Note: The eigenvectors above form an orthonormal eigenbasis for A.
=
=
Transcribed Image Text:Find the eigenvalues λ₁ < λ₂ < λ3 and associated unit eigenvectors ₁, 2, 3 of the symmetric matrix 0 0 4 ^-| 0-2 4 00 The eigenvalue ₁ = has associated unit eigenvector ₁ = The eigenvalue 1₂ has associated unit eigenvector ₂ = The eigenvalue 13 has associated unit eigenvector uz Note: The eigenvectors above form an orthonormal eigenbasis for A. = =
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