<s>[INST] Find $x$ and $y$ in a simple matrix I've just started learning matrices, but I'm not sure how to go about solving this:
$\begin{pmatrix} 1 & 2 & 0 \\ 2 & 0 & 1\\1&0&2\end{pmatrix}$
$\begin{pmatrix} 0\\ x\\ y\end{pmatrix}$ $=$ $\begin{pmatrix} 6\\2\\4\end{pmatrix}$
I'm told to use the gaussian method, but I'm getting confused with the $\begin{pmatrix} 0\\ x\\ y\end{pmatrix}$  column, every example video online that shows how to solve matrices, does not have such a column, I'm not sure what to do, any help would be appreciated. 
 [/INST] Multiply out the matrix to obtain a system of linear equations:
$\begin{bmatrix} 1 & 2 & 0 \\ 2 & 0 & 1\\1&0&2\end{bmatrix}$
$\begin{bmatrix} 0\\ x\\ y\end{bmatrix}$ $=$ $\begin{bmatrix} 6\\2\\4\end{bmatrix}\equiv$$
\left\{ 
\begin{array}{c}
1\cdot 0+2x+0y=6 \\ 
2\cdot 0+0x+1y=2 \\ 
1\cdot 0+0x+2y=4
\end{array}
\right. 
\equiv$$
\left\{ 
\begin{array}{c}
2x=6 \\ 
1y=2 \\ 
2y=4
\end{array}
\right.$
$$\implies x=3, y=2$$ (assuming there was no typo)
</s>