The matrix A is singular, with rank 1. Find its eigenvalues and associated eigenvectors. 8 -2 41 A = |-4 1 -2 8 -2 4
The matrix A is singular, with rank 1. Find its eigenvalues and associated eigenvectors. 8 -2 41 A = |-4 1 -2 8 -2 4
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CR: Review Exercises
Problem 65CR: Determine all nn symmetric matrices that have 0 as their only eigenvalue.
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![The matrix \( A \) is singular, with rank 1. Find its eigenvalues and associated eigenvectors.
\[
A = \begin{bmatrix}
8 & -2 & 4 \\
-4 & 1 & -2 \\
8 & -2 & 4
\end{bmatrix}
\]
This matrix is a 3x3 singular matrix, meaning that at least one of its eigenvalues will be zero. The problem requires finding both the eigenvalues and the corresponding eigenvectors. The structure of the matrix indicates some repetition in the rows, which is a hint towards its singularity and affects the calculation of the eigenvectors.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7297a90f-0927-4369-b782-4368eb3beb88%2Fb7b9f623-672c-4940-946c-0868c7d70009%2Fbaoaes9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The matrix \( A \) is singular, with rank 1. Find its eigenvalues and associated eigenvectors.
\[
A = \begin{bmatrix}
8 & -2 & 4 \\
-4 & 1 & -2 \\
8 & -2 & 4
\end{bmatrix}
\]
This matrix is a 3x3 singular matrix, meaning that at least one of its eigenvalues will be zero. The problem requires finding both the eigenvalues and the corresponding eigenvectors. The structure of the matrix indicates some repetition in the rows, which is a hint towards its singularity and affects the calculation of the eigenvectors.
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