Question

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

Answer 1

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

Now consider $A^T-B^T$ that is

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

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