Following the algorithm of Theorem REMEF, and working to create pivot columns from left to right, we have
\begin{align*}
\begin{bmatrix}
1 & 1 & 1 \\
-4 & -3 & -2 \\
3 & 2 & 1
\end{bmatrix}
\xrightarrow{\rowopadd{4}{1}{2}}
&
\begin{bmatrix}
1 & 1 & 1 \\
0 & 1 & 2 \\
3 & 2 & 1
\end{bmatrix}
\xrightarrow{\rowopadd{-3}{1}{3}}
\begin{bmatrix}
\leading{1} & 1 & 1 \\
0 & 1 & 2 \\
0 & -1 & -2
\end{bmatrix}\\
\xrightarrow{\rowopadd{-1}{2}{1}}
&
\begin{bmatrix}
\leading{1} & 0 & -1 \\
0 & 1 & 2 \\
0 & -1 & -2
\end{bmatrix}
\xrightarrow{\rowopadd{1}{2}{3}}
\begin{bmatrix}
\leading{1} & 0 & -1 \\
0 & \leading{1} & 2 \\
0 & 0 & 0
\end{bmatrix}
\end{align*}