Suppose $\textsf{W} = \{v\in\Bbb{R}^4 :\, a^tv=0\}$, where
$$a=\begin{bmatrix}2\\-1\\3\\-5 \\ \end{bmatrix}$$
I understand that $\textsf{W}$ can be interpreted as the nullspace of a matrix, but I don't understand how to interpret this notation such that I can use it quantitativly. 

How would one go about finding the original matrix that $\textsf{W}$ is the nullspace of; additionally, how would one find the basis $S$ of $\textsf{W}$. 

I don't understand where to begin when using notation like this. Thanks!