I was looking through my textbook and they were doing gaussian elimination on one of the rows, but I have no idea how they got to the next row. I have never done gaussian elimination with imaginary number, i. Say if my first column consists of $[1,i,0]$ and I want to get rid of the $i$. Can I multiply the row $i$ is in by $i$ to get $i^2 =-1$ and then work my way from their? Does $i$ and any variation of $i$ still count as a valid scalar to multiply by?
2026-03-27 15:16:19.1774624579
imaginary (Complex) numbers and matrices
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The elementary row operations include operations like $R_i + cR_j$ and $cR_i$.
For the purpose of solving linear equation involving complex number, $c$ can be any non-zero complex number, and this would include $i$.
For $[1,i,0]$ being in the first row, you should choose $c$ in $R_i + cR_j$ such that it eliminates the first entry of another row.