Let $A = \left[{\begin{matrix}5 & 10 & 5 & 25 \cr 2 & 6 & 6 & 16 \cr 3 & 1 & -8 & -3 \cr 5 & 9 & 1 & 16 \cr \end{matrix}}\right]$.

We want to determine if the columns of $A$ span ${\mathbb R}^3$.

To check this we add times the first row to the second.
We then add times the first row to the third.
We then add times the first row to the fourth.
We then add times the new second row to the new third row.
We then add times the new second row to the new fourth row.
Finally then add times the new third row to the new fourth row.

We conclude that

A. The columns of $A$ do not span ${\mathbb R}^4$.
B. The columns of $A$ do span ${\mathbb R}^4$.
C. We cannot tell if the columns of $A$ span ${\mathbb R}^4$.