Q:

Determine what $\dim(X)$ is.

How would I determine the dimension of the following subspace?  
$$X=\left\{\ \begin {pmatrix} -ix\\ 3x \\ i^2x \end{pmatrix} \in \mathbb{C^3} \ \biggm| x \in \mathbb {C}  \right\}\subseteq\mathbb{C}^3$$
I'm unsure as to how to start my solution so any hints would be great!

A:

$$
\begin {pmatrix} -ix\\ 3x \\ i^2x \end{pmatrix} = x \begin {pmatrix} -i \\ 3 \\ i^2 \end{pmatrix}
$$
There's only one "free" variable.

