Exercise 1.3.2

Determine the transpose of each of the matrices that follow. In addition, if the matrix is square, compute its trace.

(a)

$\left(\begin{array}{cc}\hfill -4& \hfill 2\\ \hfill 5& \hfill -1\end{array}\right)$

(b)

$\left(\begin{array}{ccc}\hfill 0& \hfill 8& \hfill -6\\ \hfill 3& \hfill 4& \hfill 7\end{array}\right)$

(c)

$\left(\begin{array}{cc}\hfill -3& \hfill 9\\ \hfill 0& \hfill -2\\ \hfill 6& \hfill 1\end{array}\right)$

(d)

$\left(\begin{array}{ccc}\hfill 10& \hfill 0& \hfill -8\\ \hfill 2& \hfill -4& \hfill 3\\ \hfill -5& \hfill 7& \hfill 6\end{array}\right)$

(e)

$\left(\begin{array}{cccc}1\hfill & -1\hfill & 3\hfill & 5\hfill \end{array}\right)$

(f)

$\left(\begin{array}{cccc}\hfill -2& \hfill 5& \hfill 1& \hfill 4\\ \hfill 7& \hfill 0& \hfill 1& \hfill -6\end{array}\right)$

(g)

$\left(\begin{array}{c}5\hfill \\ 6\hfill \\ 7\hfill \end{array}\right)$

(h)

$\left(\begin{array}{ccc}\hfill -4& \hfill 0& \hfill 6\\ \hfill 0& \hfill 1& \hfill -3\\ \hfill 6& \hfill -3& \hfill 5\end{array}\right)$