The augmented matrix for the given linear system and its row-reduced form are:
\begin{align*}
\begin{bmatrix}
1 & -2 & 1 & -1 & 2\\
1 & 1 & 1 & -1 & 2\\
1 & 0 & 1 & -1 & 2
\end{bmatrix}
\rref
\begin{bmatrix}
\leading{1} & 0 & 1 & -1 & 2\\
0 & \leading{1} & 0 & 0 & 0\\
0 & 0 & 0 & 0 & 0
\end{bmatrix}.
\end{align*}
Thus, we see that an equivalent system is
\begin{align*}
x_1 &= 2 - x_3 + x_4\\
x_2 &= 0,
\end{align*}
and the solution set is
$\setparts{\colvector{2 - x_3 + x_4\\ 0 \\ x_3 \\ x_4}}{x_3, x_4 \in\complexes}$. For this system, $n = 4$ and $r = 2$. Since it is a consistent system by Theorem RCLS, Theorem CSRN guarantees an infinite number of solutions.