Question

Please solve the below problem:

Answer 1

Given, $A = \left[\begin{array}{cc}3&3\\7&6\end{array}\right]$
$B = \left[\begin{array}{cc}8&7\\0&9\end{array}\right]$
And $C = \left[\begin{array}{cc}2&-3\\4&6\end{array}\right]$

Now, A + B = $\left[\begin{array}{cc}3&3\\7&6\end{array}\right] +\left[\begin{array}{cc}8&7\\0&9\end{array}\right]=\left[\begin{array}{cc}3+8&3+7\\7+0&6+9\end{array}\right]\\\\=\left[\begin{array}{cc}11&10\\7&15\end{array}\right]$
Now, (A + B)C = $\left[\begin{array}{cc}11&10\\7&15\end{array}\right].\left[\begin{array}{cc}2&-3\\4&6\end{array}\right]=\left[\begin{array}{cc}11.2+10.4&11.-3+10.6\\7.2+15.4&7.-3+15.6\end{array}\right]\\\\=\left[\begin{array}{cc}62&27\\74&69\end{array}\right]$

Now, Similarly find out AC + BC = $\left[\begin{array}{cc}18&9\\38&15\end{array}\right]+\left[\begin{array}{cc}44&18\\36&54\end{array}\right]=\left[\begin{array}{cc}62&27\\74&69\end{array}\right]$

And also you can see , (A + B)C = AC + BC .

Answer 2

solution:-

see attch file