Example Find the sum of the matrix $A$ and $B$.

$\displaystyle A = \left(\begin{array}{rr}
2&-3\\
4&2
\end{array}\right), \ \ \ B = \left(\begin{array}{rr}
-1&2\\
3&0
\end{array}\right ) $

Answer We define the sum of $A = (a_{ij})$ and $B = (b_{ij})$ by $(a_{ij}+b_{ij})$. Thus, we add the corresponding elements of $A$ and $B$.

$A + B = \left(\begin{array}{rr}
2&\!\!-3\\
4&\!\!2
\end{array}\right) + \left(...
...ay}\right) = \left(\begin{array}{rr}
1&\!\!-1\\
7&\!\!2
\end{array}\right ) . $