Answer
Yes, see solution
Work Step by Step
Let A be matrix $\begin{bmatrix}
1&-5&7\\
1&-1&0\\
-2&2&-5
\end{bmatrix}$~$\begin{bmatrix}
1&0&0\\
0&1&0\\
0&0&1
\end{bmatrix}$
Columns of A span $R^2$ if A is invertible by Theorem 8 because the columns of A form a linearly independent set.