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 - Page 61: 3

Answer

No, the vectors are not linearly independent.

Work Step by Step

According to the box on page 59, two vectors are linearly dependent if one is a constant multiple of the other. In this case, $ -3\begin{bmatrix}1\\-3\end{bmatrix}=\begin{bmatrix}-3\\9\end{bmatrix}$, so the vectors are linearly dependent. This solution may be confirmed by row-reducing the matrix whose columns are the given vectors, as the resulting echelon matrix will not have a pivot in the second column.
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