Let $A = \left[{\begin{matrix}2 & 4 & 2 \cr 3 & 9 & 18 \cr 4 & 10 & 16 \cr \end{matrix}}\right]$.

We want to determine if the columns of matrix $A$ are linearly independent. To do that we row reduce $A$. Here is one way to row reduce it.

First, we can add times the first row to the second.
We then would add times the first row to the third.
We then can add times the new second row to the new third row.
We conclude that

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