A matrix with more than $m$ columns may have more than one set of $m$-dimensional vectors with $m$ mutually linearly independent columns?

Question

Chapter 2.4 (Linear Dependence and Span), page 36 of Deep Learning by Goodfellow, Bengio, and Courville, claims the following:

No set of $m$-dimensional vectors can have more than $m$ mutually linearly independent columns, but a matrix with more than $m$ columns may have more than one such set.

I understand that no set of $m$-dimensional vectors can have more than $m$ mutually linearly independent columns, but I'm unsure of what the latter claim is trying to say.

It's probably the way that this is phrased that is confusing me, so I would appreciate it if people could please take the time to clarify this.

Answer 1

A 4x8 matrix may have many sets of 4 linearly independent columns. Perhaps the first 4 columns are independent, and so are the last 4 columns

Answer 2

Try a simple example: any pair of columns of the matrix $\begin{bmatrix}1&0&1\\0&1&1\end{bmatrix}$ that you choose are linearly independent.