The set of vectors $\left\{ \begin{pmatrix} 1 \\ 2 \end{pmatrix}, \begin{pmatrix} 3 \\ k \end{pmatrix} \right\}$ is linearly dependent.  Find all possible values of $k.$  Enter all the possible values, separated by commas.
Linearly dependent means that one vector is a scalar multiple of the other. So, I need to find $k$ such that $\begin{pmatrix} 3 \\ k \end{pmatrix} = c \begin{pmatrix} 1 \\ 2 \end{pmatrix}$ for some constant $c.$ This implies that $3 = c$ and $k = 2c.$ Therefore, $k = 2 \cdot 3 = 6.$ 