$\displaystyle

\left\{

\begin{matrix}

ax - 3y + z = a\\

-x + 6y = -2\\

x + 5z = 4\\

\end{matrix}\right.

$

system matrix:

$\displaystyle

\[

A =

\left[ \begin{array}{ccc|c}

a & -3 & 1 & a\\

-1 & 6 & 0 & -2\\

1 & 0 & 5 & 4\end{array}\right]

$

I'm not sure where to start. Should I switch row 3 and row 1?