How can the "vector of the unknowns" in matrix be a true vector?

In linear algebra,if
$$\begin{cases}
x-3y=-1 \\
x+y=2\end{cases}$$
then the system can be written as $Av=b$, where $A= \begin{bmatrix}1 & -3\\1 & 1\end{bmatrix}$ , $v = \begin{bmatrix}x \\ y\end{bmatrix}$ and 
$b = \begin{bmatrix} -1 \\ 2 \end{bmatrix}$. 

And this $v$ is called the vector of the unknowns.

But a vector should have length and a size, right? So how can this be a true "vector"? $\begin{bmatrix}x \\ y\end{bmatrix}$ does not have a set length or a size; rather, it is inherently undefined, or incomplete, in my opinion. (It is not possible to draw $\begin{bmatrix}x \\ y\end{bmatrix}$).