Answer
$2A-5B=\begin{bmatrix}
21 & 3
\\
2 & 16
\\
7 & -25
\end{bmatrix}$
Work Step by Step
Multiplying each element of $A=
\begin{bmatrix}
3 & 4
\\
6 & -2
\\
1 & 0
\end{bmatrix}
$ by $2,$ and then subtracting the result to $5$ times each element of $B=
\begin{bmatrix}
-3 & 1
\\
2 & -4
\\
-1 & 5
\end{bmatrix}
,$ then
\begin{align*}
2A-5B&=
\begin{bmatrix}
3(2) & 4(2)
\\
6(2) & -2(2)
\\
1(2) & 0(2)
\end{bmatrix}
-
\begin{bmatrix}
-3(5) & 1(5)
\\
2(5) & -4(5)
\\
-1(5) & 5(5)
\end{bmatrix}
\\\\&=
\begin{bmatrix}
6 & 8
\\
12 & -4
\\
2 & 0
\end{bmatrix}
-
\begin{bmatrix}
-15 & 5
\\
10 & -20
\\
-5 & 25
\end{bmatrix}
\\\\&=
\begin{bmatrix}
6-(-15) & 8-5
\\
12-10 & -4-(-20)
\\
2-(-5) & 0-25
\end{bmatrix}
\\\\&=
\begin{bmatrix}
6+15 & 8-5
\\
12-10 & -4+20
\\
2+5 & 0-25
\end{bmatrix}
\\\\&=
\begin{bmatrix}
21 & 3
\\
2 & 16
\\
7 & -25
\end{bmatrix}
.\end{align*}
Hence, $
2A-5B=\begin{bmatrix}
21 & 3
\\
2 & 16
\\
7 & -25
\end{bmatrix}
.$
