Show all your work. 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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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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The matrix A is singular, with rank 1. Find its eigenvalues and associated eigenvectors. 8 -2 41 A = |-4 1 -2 8 -2 4