Let ${\bf u} = \left[{\begin{matrix}2 \cr 3 \cr \end{matrix}}\right]$, and ${\bf v} = \left[{\begin{matrix}4 \cr 9 \cr \end{matrix}}\right]$.

We want to determine if $\lbrace{{\bf u}, {\bf v}}\rbrace$ is linearly independent. To do that we write the vectors as columns of a matrix $A$ and row reduce that matrix.

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

A. The set $\lbrace{{\bf u}, {\bf v}}\rbrace$ is linearly independent.
B. The set $\lbrace{{\bf u}, {\bf v}}\rbrace$ is linearly dependent.
C. We cannot tell if the set $\lbrace{{\bf u}, {\bf v}}\rbrace$ is linearly independent or not.