Answer
$3A+2B=\begin{bmatrix}
3 & 14
\\
22 & -14
\\
1 & 10
\end{bmatrix}
$
Work Step by Step
Multiplying each element of $A=
\begin{bmatrix}
3 & 4
\\
6 & -2
\\
1 & 0
\end{bmatrix}
$ by $3,$ and then adding the result to $2$ times each element of $B=
\begin{bmatrix}
-3 & 1
\\
2 & -4
\\
-1 & 5
\end{bmatrix}
,$ then
\begin{align*}
3A+2B&=
\begin{bmatrix}
3(3) & 4(3)
\\
6(3) & -2(3)
\\
1(3) & 0(3)
\end{bmatrix}
+
\begin{bmatrix}
-3(2) & 1(2)
\\
2(2) & -4(2)
\\
-1(2) & 5(2)
\end{bmatrix}
\\\\&=
\begin{bmatrix}
9 & 12
\\
18 & -6
\\
3 & 0
\end{bmatrix}
+
\begin{bmatrix}
-6 & 2
\\
4 & -8
\\
-2 & 10
\end{bmatrix}
\\\\&=
\begin{bmatrix}
9+(-6) & 12+2
\\
18+4 & -6+(-8)
\\
3+(-2) & 0+10
\end{bmatrix}
\\\\&=
\begin{bmatrix}
9-6 & 12+2
\\
18+4 & -6-8
\\
3-2 & 0+10
\end{bmatrix}
\\\\&=
\begin{bmatrix}
3 & 14
\\
22 & -14
\\
1 & 10
\end{bmatrix}
.\end{align*}
Hence, $
3A+2B=\begin{bmatrix}
3 & 14
\\
22 & -14
\\
1 & 10
\end{bmatrix}
.$
