Answer
$\left[\begin{array}{rr}
50 & -3\\
18 & 21
\end{array}\right]$
Work Step by Step
$A+B=\left[\begin{array}{lll}
0+4 & 3+1 & -5+0\\
1+(-2) & 2+3 & 6+(-2)
\end{array}\right]$
$=\left[\begin{array}{lll}
4 & 4 & -5\\
-1 & 5 & 4
\end{array}\right]$
(A+B) is a 2 by 3 matrix. C is a 3 by 2 matrix.
(A+B)C is defined and is a 2 by 2 matrix,
the entry $[(A+B)C]_{ij}$ = (row i of $A+B$)$\times$(column j of $C $) .
$(A+B)C=\left[\begin{array}{lll}
4 & 4 & -5\\
-1 & 5 & 4
\end{array}\right]\left[\begin{array}{ll}
4 & 1\\
6 & 2\\
-2 & 3
\end{array}\right]$
$=\left[\begin{array}{ll}
16+24+10 & 4+8-15\\
-4+30-8 & -1+10+12
\end{array}\right]$
$=\left[\begin{array}{ll}
50 & -3\\
18 & 21
\end{array}\right]$
