Question

Let $A=\left[\begin{array}{ccc}1& -1& 2\\ 2& 1& 0\end{array}\right],B=\left[\begin{array}{ccc}0& 1& -1\\ 1& 2& 3\end{array}\right],\text{and}C=\left[\begin{array}{ccc}-1& 2& 3\\ 0& 0& 1\end{array}\right]$

Find each of the following :

(iv) $B+C$

Answer 1

Addition of matrices $B\text{and}C$.

The addition of matrices is defined as the addition of corresponding elements of two or more matrices having the same order.

$\begin{array}{rcl}B+C& =& \left[\begin{array}{ccc}0& 1& -1\\ 1& 2& 3\end{array}\right]+\left[\begin{array}{ccc}-1& 2& 3\\ 0& 0& 1\end{array}\right]\\ & =& \left[\begin{array}{ccc}0-1& 1+2& -1+3\\ 1+0& 2+0& 3+1\end{array}\right]\\ & =& \left[\begin{array}{ccc}-1& 3& 2\\ 1& 2& 4\end{array}\right]\end{array}$

Final answer: The sum is $\begin{array}{l}\left[\begin{array}{ccc}-1& 3& 2\\ 1& 2& 4\end{array}\right]\end{array}$.