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 62: 29


$ \mathbf{A}=\begin{bmatrix}2&4\\3&7\\5&9\end{bmatrix} $, $ \mathbf{B}=\begin{bmatrix}1&2\\2&4\\3&6\end{bmatrix} $

Work Step by Step

In general, $\mathbf{A}$ must have linearly independent columns, and $\mathbf{B}$ must have linearly dependent columns. To achieve this, we make sure that the columns of $\mathbf{A}$ are not multiples of one another, but that the columns of $\mathbf{B}$ are.
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