Question

If $A=\left[\begin{array}{cc}3& 7\\ 2& 5\end{array}\right]$ and $B=\left[\begin{array}{cc}-3& 2\\ 4& -1\end{array}\right]$ find the matrix $C$ if $2C=A+B$

Answer 1

$A+B=\left[\begin{array}{cc}3& 7\\ 2& 5\end{array}\right]+\left[\begin{array}{cc}-3& 2\\ 4& -1\end{array}\right]$

$A+B=\left[\begin{array}{cc}3-3& 7+2\\ 2+4& 5-1\end{array}\right]$

$A+B=\left[\begin{array}{cc}0& 9\\ 6& 4\end{array}\right]$

$\Rightarrow A+B=2C=\left[\begin{array}{cc}0& 9\\ 6& 4\end{array}\right]$

$\Rightarrow C=\frac{1}{2}\left[\begin{array}{cc}0& 9\\ 6& 4\end{array}\right]$

$\Rightarrow C=\left[\begin{array}{cc}0& \frac{9}{2}\\ 3& 2\end{array}\right]$

Thus, the matrix $C=\left[\begin{array}{cc}0& \frac{9}{2}\\ 3& 2\end{array}\right]$