Chapter 2.2, Problem 2P

For problems 1-2, let

$A=\left[\begin{array}{ccc}-2& 6& 1\\ -1& 0& -3\end{array}\right]$, $B=\left[\begin{array}{ccc}2& 1& -1\\ 0& 4& -4\end{array}\right]$, $C=\left[\begin{array}{cc}1+i& 2+i\\ 3+i& 4+i\\ 5+i& 6+i\end{array}\right]$, $D=\left[\begin{array}{ccc}4& 0& 1\\ 1& 2& 5\\ 3& 1& 2\end{array}\right]$, $E=\left[\begin{array}{ccc}2& -5& -2\\ 1& 1& 3\\ 4& -2& -3\end{array}\right]$, $F=\left[\begin{array}{ccc}6& 2-3i& i\\ 1+i& -2i& 0\\ -1& 5+2i& 3\end{array}\right]$.

In these problems, i denotes $\sqrt{-1}$.

Compute each of the following:

(a) $-D$

(b) $4B^T$

(c) $-2A^T+C$

(d) $5E+D$

(e) $4A^T-2B^T+iC$

(f) $4E-3D^T$

(g) $\left(1-6i\right)F+iD$

(h) the matrix G such that $2A-B+\left(1+i\right)C^T=G+A-B$

(i) the matrix H such that $3D-3E+6I_3-2H=0_3$

(j) the matrix K such that $K^T+F^T=D^T+E^T$