<s>[INST] Gaussian elimination-complex numbers How a row of zero can be reached with this matrix....$\begin{pmatrix}1-i&0&-1\\1&-i&0\\1&-1&-i\end{pmatrix}$I have used conjugate of the complex number, but I can't reach the right answer....may you please show me the way?
 [/INST] $$
\begin{align}
\begin{bmatrix}
1-i & 0 & -1 \\
1 & -i & 0 \\
1 & -1 & -i
\end{bmatrix}
&\sim
\begin{bmatrix}
1-i & 0 & -1 \\
1 & -i & 0 \\
0 & -1+i & -i
\end{bmatrix} && {\color{blue}{(3):=(3)-(2)}}\\
&\sim
\begin{bmatrix}
1-i & 0 & -1 \\
1-i & -1-i & 0 \\
0 & -1+i & -i
\end{bmatrix} && \color{blue}{(2):=(1-i)\times(2)}\\
&\sim
\begin{bmatrix}
1-i & 0 & -1 \\
0 & -1-i & 1 \\
0 & -1+i & -i
\end{bmatrix} && \color{blue}{(2):=(2)-(1)}\\
&\sim
\begin{bmatrix}
1-i & 0 & -1 \\
0 & -1-i & 1 \\
0 & -1-i & 1
\end{bmatrix} && \color{blue}{(3):=i\times(3)}\\
&\sim
\begin{bmatrix}
1-i & 0 & -1 \\
0 & -1-i & 1 \\
0 & 0 & 0
\end{bmatrix} && \color{blue}{(3):=(3)-(2)}
\end{align}
$$
</s>