## Linear Algebra and Its Applications (5th Edition)

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