Let $A = \left[{\begin{matrix}2 & 4 \cr 5 & 12 \cr \end{matrix}}\right]$.

We want to determine if the columns of matrix $A$ and are linearly independent. To do that we row reduce $A$.

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

A. The columns of $A$ are linearly dependent.
B. The columns of $A$ are linearly independent.
C. We cannot tell if the columns of $A$ are linearly independent or not.