Question

Find the transpose of each of the following matrices:
$\left(i\right)$ $\left[\begin{array}{c}5\\ \frac{1}{2}\\ -1\end{array}\right]$

$\left(ii\right)$ $\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$

$\left(iii\right)$ $\left[\begin{array}{c}-1\\ \sqrt{3}\\ 2\end{array}\begin{array}{c}5\\ 5\\ 3\end{array}\begin{array}{c}6\\ 6\\ -1\end{array}\right]$

Answer 1

$\left(i\right)$ Let $A=\left[\begin{array}{c}5\\ \frac{1}{2}\\ -1\end{array}\right]$ , then $A^T=\left[\begin{array}{ccc}5& \frac{1}{2}& -1\end{array}\right]$

$\left(ii\right)$ Let $A=\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$, then $A^T=\left[\begin{array}{cc}1& 2\\ -1& 3\end{array}\right]$

$\left(iii\right)$ Let $A=\left[\begin{array}{c}-1\\ \sqrt{3}\\ 2\end{array}\begin{array}{c}5\\ 5\\ 3\end{array}\begin{array}{c}6\\ 6\\ -1\end{array}\right]$ , then $A^T=\left[\begin{array}{c}-1\\ 5\\ 6\end{array}\begin{array}{c}\sqrt{3}\\ 5\\ 6\end{array}\begin{array}{c}2\\ 3\\ -1\end{array}\right]$