8. Find the linear combination $3 A-2 B$, if

$$
A=\left(\begin{array}{rrr}
2 & -4 & 0 \\
-1 & 5 & 1 \\
0 & 3 & -7
\end{array}\right), \quad B=\left(\begin{array}{rrr}
4 & -1 & -2 \\
0 & -3 & 5 \\
2 & 0 & -4
\end{array}\right)
$$
Solution. First, we find the product of $A$ by $k_{1}=3$ and $B$ by $k_{2}=-2$:

$$
3 A=\left(\begin{array}{rrr}
6 & -12 & 0 \\
-3 & 15 & 3 \\
0 & 9 & -21
\end{array}\right), \quad-2 B=\left(\begin{array}{rrr}
-8 & 2 & 4 \\
0 & 6 & -10 \\
-4 & 0 & 8
\end{array}\right)
$$

Now let's find the sum of the obtained matrices:

$$
3 A-2 B=\left(\begin{array}{rrc}
6-8 & -12+2 & 0+4 \\
-3+0 & 15+6 & 3-10 \\
0-4 & 9+0 & -21+8
\end{array}\right)=\left(\begin{array}{rrr}
-2 & -10 & 4 \\
-3 & 21 & -7 \\
-4 & 9 & -13
\end{array}\right)
$$

9-11. Calculate the linear combinations of matrices: