Linear Algebra and Its Applications (5th Edition)

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

Chapter 1 - Linear Equations in Linear Algebra - 1.7 Exercises - Page 62: 17

Answer

The vectors are linearly dependent.

Work Step by Step

The given set of vectors $\begin{bmatrix} 3 \\ 5\\ -1\\ \end{bmatrix}$, $\begin{bmatrix} 0 \\ 0\\ 0\\ \end{bmatrix}$, $\begin{bmatrix} -6 \\ 5\\ 4\\ \end{bmatrix}$ contains the zero vector, so by Theorem 9, the set of vectors is automatically linearly dependent. .
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