Reducing to upper triangular form I've just had some difficulty with this transforming this matrix into upper triangular form:
$$
\pmatrix{
i& 2i& -1\\1 & 1& i\\ 2-i& 1&  i
}
$$
I've tried almost everything. I've multiplied the second row by $i$ to try and eliminate the complex in the first column but no avail. I've also tried using the first row to eliminate the complex in the last row but that hasn't worked out yet either. I just don't know whether I'm even starting it out correctly or whether I've made some errors in my calculations.

$$
\pmatrix{i&2i&-1\\1&1&i\\2-i&1&i}
\stackrel{(2):=(2)+i(1)}\sim
\pmatrix{i&2i&-1\\0&-1&0\\2-i&1&i}
\stackrel{(3):=(3)+(1+2i)(1)}\sim
\pmatrix{i&2i&-1\\0&-1&0\\0&2i-3&-1-i}
\stackrel{(3):=(3)+(2i-3)(2)}\sim
\pmatrix{i&2i&-1\\0&-1&0\\0&0&-1-i}.
$$
