Find the eigenvalues A1 < A2 < A3 and associated unit eigenvectors 1, 2, 3 of the symmetric matrix 1 11 A = 4 -2 4 4 The eigenvalue A₁ = has associated unit eigenvector i The eigenvalue ₂ = has associated unit eigenvector 2 = 9. The eigenvalue 3: = has associated unit eigenvector 3 = Note: The eigenvectors above form an orthonormal eigenbasis for A.
Find the eigenvalues A1 < A2 < A3 and associated unit eigenvectors 1, 2, 3 of the symmetric matrix 1 11 A = 4 -2 4 4 The eigenvalue A₁ = has associated unit eigenvector i The eigenvalue ₂ = has associated unit eigenvector 2 = 9. The eigenvalue 3: = has associated unit eigenvector 3 = 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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Question
![Find the eigenvalues A1 < A2 < A3 and associated unit eigenvectors 1, 2, 3 of the
symmetric matrix
1
11
A = 4
-2 4
4
The eigenvalue A₁
=
has associated unit eigenvector i
The eigenvalue ₂ =
has associated unit eigenvector 2 =
9.
The eigenvalue 3:
=
has associated unit eigenvector 3 =
Note: The eigenvectors above form an orthonormal eigenbasis for A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef19df16-a9cf-4d28-80b1-5d3bd6b485e3%2Fd72bd0c2-5c7a-4307-9898-ed6bd91ce85a%2Fg8ozvbn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the eigenvalues A1 < A2 < A3 and associated unit eigenvectors 1, 2, 3 of the
symmetric matrix
1
11
A = 4
-2 4
4
The eigenvalue A₁
=
has associated unit eigenvector i
The eigenvalue ₂ =
has associated unit eigenvector 2 =
9.
The eigenvalue 3:
=
has associated unit eigenvector 3 =
Note: The eigenvectors above form an orthonormal eigenbasis for A.
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