Linear Algebra and Its Applications (5th Edition)

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

Chapter 1 - Linear Equations in Linear Algebra - 1.7 Exercises: 14

Answer

$h=26$

Work Step by Step

The vectors are linearly dependent if and only if the matrix equation $\mathbf{A}\vec{x}=\vec{0}$ has a nontrivial solution, where $\mathbf{A}$ is the matrix whose columns are the given vectors. By row reduction, we conclude that $\begin{bmatrix}1&-5&1\\-1&7&1\\3&8&h\end{bmatrix}\sim\begin{bmatrix}1&-5&1\\0&1&1\\0&0&h-26\end{bmatrix}$. Since the homogeneous matrix equation has a nontrivial solution if and only if at least one column of the coefficient matrix lacks a pivot, we set $h=26$, making the final row all zeros and providing a free variable in the third column.
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.