**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].

$$