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 :

(v) $A+\left(B+C\right)$

Answer 1

Calculation of the matrix $A+\left(B+C\right)$.

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

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

Final answer: The sum is $\left[\begin{array}{ccc}0& 2& 4\\ 3& 3& 4\end{array}\right]$.