Question

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

Answer 1

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

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

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

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

$=\left[\begin{array}{cc}4& 3\\ -3& 0\\ -1& -2\end{array}\right]$

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