Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 5 - Eigenvalues and Eigenvectors - 5.1 Exercises - Page 273: 2

Answer

$λ=-2$ is an eigenvalue

Work Step by Step

Given $$A=\begin{pmatrix}7&3\\3&-1 \end{pmatrix} $$ Since the characteristic equation \begin{align*} |A-\lambda I|&=0\\ \left| \begin{array}{rr} 7-\lambda&3\\3&-1-\lambda \end{array}\right|&=0\\ \left(7-λ\right)\left(-1-λ\right)-3\cdot \:3&=0\\ λ^2-6λ-16&=0\\ (-2)^2 - 6(-2) - 16 = \\ 4 + 12 - 16= \\ 16-16 = 0, \end{align*} Therefore $λ=-2$ satisfies the characteristic equation and $λ=-2$ is an eigenvalue of the given matrix
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.