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Find a row-reduced matrix to the given one

Solution to Linear Algebra Hoffman & Kunze Chapter 1.3 Exercise 1.3.4

Solution: We have $$A\rightarrow\left[\begin{array}{ccc} 1 & -2 & 1\\ i & -(1+i) & 0\\ 1 & 2i & -1 \end{array}\right]\rightarrow \left[\begin{array}{ccc} 1 & -2 & 1\\ 0 & -1+i & -i\\ 0 & 2+2i & -2 \end{array}\right]\rightarrow \left[\begin{array}{ccc} 1 & -2 & 1\\ 0 & 1 & \frac{1-i}2\\ 0 &2+ 2i & -2 \end{array}\right]$$ $$\rightarrow \left[\begin{array}{ccc} 1 & -2 & 1\\ 0 & 1 & \frac{i-1}2\\ 0 & 0 & 0 \end{array}\right]\rightarrow \left[\begin{array}{ccc} 1 & 0 & i\\ 0 & 1 & \frac{i-1}2\\ 0 & 0 & 0 \end{array}\right].$$