Find all the solutions of the system $AX=B$ if $B$ is the difference between the first and the fourth column of $A$. Let 
$$A \sim
\begin{pmatrix}
1 &2 &4&1\\
0&0&1&2\\
1&3&1&1\\
0&0&0&0\\
\end{pmatrix}$$
such that the equivalence is achieved by elementary row transformations. Find all the solutions of the system $AX=B$ if $B$ is the difference between the first and the fourth column of $A$.
I hope I understood this: $$B=\begin{pmatrix}
0\\
-2\\
0\\
0
\end{pmatrix}$$
But I don't know what should I do here since I don't know what $A$ is exactly...I know $X$ should be a $4$x$1$ matrix and that's about it.

Hint -
You have A and B. 
Solve AX = B.
$$\begin{pmatrix}
1 &2 &4&1\\
0&0&1&2\\
1&3&1&1\\
0&0&0&0\\
\end{pmatrix} \cdot \begin{pmatrix}
x_1\\
x_2\\
x_3\\
x_4
\end{pmatrix} = \begin{pmatrix}
0\\
-2\\
0\\
0
\end{pmatrix}$$
