Answer
See below
Work Step by Step
$\begin{bmatrix}
1& 1+i & 1-i|0\\i & 1 & i |0 \\1-2i & i-1&1-3i|0
\end{bmatrix} \approx \begin{bmatrix}
1& 1+i & 1-i|0\\0& 2-i & -1 |0 \\0 & 2i-4& 2|0
\end{bmatrix} \approx \begin{bmatrix}
1& 1+i & 1-i|0\\0& 2-i & -1 |0 \\0 & 0 & 0|0
\end{bmatrix} \approx \begin{bmatrix}
1& 1+i & 1-i|0\\0& 1 & -\frac{-2-i}{5} |0 \\0 & 0 & 0|0
\end{bmatrix} \approx \begin{bmatrix}
1& 0 & \frac{6-2i}{5}|0\\0& 1 & \frac{-2-i}{5} |0 \\0 & 0 & 0|0
\end{bmatrix} $
$1.A_{12}(-i),A_{13}(2i-i)\\
2.A_{23}(2)\\
3.M_2(\frac{1}{2-i})\\
8.A_{21}(-i-1)$
We can notice that $x_3$ is a free variable, then let $x_3=5s \forall s \in C$
We have: $x_1=2(i-3)s\\
x_2=(2+i)s$
The solution set of the system is: $\{2(i-3)s,(i+2)s,5s: s\in C\}$
