Linear Algebra: A Modern Introduction

Published by Cengage Learning
ISBN 10: 1285463242
ISBN 13: 978-1-28546-324-7

Chapter 4 - Eigenvalues and Eigenvectors - 4.1 Introduction to Eigenvalues and Eigenvectors - Exercises 4.1 - Page 260: 4



Work Step by Step

If A is an nxn matrix, a scalar $\lambda$ is called an eigenvalue of A is there is a non-zero vector $v$ such that $Ax=\lambda x$. This vector is called the eigenvector of A corresponding to $\lambda$. Hence here, we compute: $Av=\begin{bmatrix} 4 &-2 \\ 5 & -7 \end{bmatrix}\cdot\begin{bmatrix} 4 \\ 2 \end{bmatrix}=\begin{bmatrix} 12\\ 6 \end{bmatrix}=3\begin{bmatrix} 4 \\ 2 \end{bmatrix}=3v$ Thus we can see that $\lambda=3$
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