Question

If $A^T=\left[\begin{array}{cc}3& 4\\ -1& 2\\ 0& 1\end{array}\right]\mathrm{and}B=\left[\begin{array}{ccc}-1& 2& 1\\ 1& 2& 3\end{array}\right]$, find A^T − B^T.

Answer 1

Given: $A^T=\left[\begin{array}{cc}3& 4\\ -1& 2\\ 0& 1\end{array}\right]\mathrm{and}B=\left[\begin{array}{ccc}-1& 2& 1\\ 1& 2& 3\end{array}\right]$

$B^T=\left[\begin{array}{cc}-1& 1\\ 2& 2\\ 1& 3\end{array}\right]$

Now,
$$\begin{gathered} A^T-B^T=\left[\begin{array}{cc}3& 4\\ -1& 2\\ 0& 1\end{array}\right]-\left[\begin{array}{cc}-1& 1\\ 2& 2\\ 1& 3\end{array}\right] \\ =\left[\begin{array}{cc}3+1& 4-1\\ -1-2& 2-2\\ 0-1& 1-3\end{array}\right] \\ =\left[\begin{array}{cc}4& 3\\ -3& 0\\ -1& -2\end{array}\right] \end{gathered}$$

Therefore, $A^T-B^T=\left[\begin{array}{cc}4& 3\\ -3& 0\\ -1& -2\end{array}\right]$.