Question

Compute the following sums:
(i) $\left[\begin{array}{cc}3& -2\\ 1& 4\end{array}\right]+\left[\begin{array}{cc}-2& 4\\ 1& 3\end{array}\right]$

(ii) $\left[\begin{array}{ccc}2& 1& 3\\ 0& 3& 5\\ -1& 2& 5\end{array}\right]+\left[\begin{array}{ccc}1& -2& 3\\ 2& 6& 1\\ 0& -3& 1\end{array}\right]$

Answer 1

$$\begin{gathered} \left(i\right)\left[\begin{array}{cc}3& -2\\ 1& 4\end{array}\right]+\left[\begin{array}{cc}-2& 4\\ 1& 3\end{array}\right] \\ \Rightarrow \left[\begin{array}{cc}3-2& -2+4\\ 1+1& 4+3\end{array}\right] \\ \Rightarrow \left[\begin{array}{cc}1& 2\\ 2& 7\end{array}\right] \end{gathered}$$

$$\begin{gathered} \left(ii\right)\left[\begin{array}{ccc}2& 1& 3\\ 0& 3& 5\\ -1& 2& 5\end{array}\right]+\left[\begin{array}{ccc}1& -2& 3\\ 2& 6& 1\\ 0& -3& 1\end{array}\right] \\ \Rightarrow \left[\begin{array}{ccc}2+1& 1-2& 3+3\\ 0+2& 3+6& 5+1\\ -1+0& 2-3& 5+1\end{array}\right] \\ \Rightarrow \left[\begin{array}{ccc}3& -1& 6\\ 2& 9& 6\\ -1& -1& 6\end{array}\right] \end{gathered}$$