Let $A = \left[{\begin{matrix}2 & 0 & 2 \cr 3 & 3 & 21 \cr \end{matrix}}\right]$.

We want to determine if the columns of $A$ span ${\mathbb R}^2$.

To check this we add times the first row to the second. We conclude that

A. The columns of $A$ do not span ${\mathbb R}^2$.
B. The columns of $A$ do span ${\mathbb R}^2$.
C. We cannot tell if the columns of $A$ span ${\mathbb R}^2$.