Linear Algebra: A Modern Introduction

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

Chapter 2 - Systems of Linear Equations - 2.3 Spanning Sets and Linear Independence - Exercises 2.3 - Page 98: 31

Answer

Linearly dependent.

Work Step by Step

We can see that $\begin{bmatrix}1\\1\\3\\1\end{bmatrix}=\begin{bmatrix}3\\-1\\1\\-1\end{bmatrix}+\begin{bmatrix}-1\\3\\1\\-1\end{bmatrix}+\begin{bmatrix}-1\\-1\\1\\3\end{bmatrix}$, thus the vectors are linearly dependent.
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