To solve the problem of multiplying the matrix by -2, we'll multiply each element of the matrix by -2. Given the matrix:
[tex]\[
\left[\begin{array}{ccc}
-3 & 5 & 1 \\
8 & -2 & 3 \\
2 & 1 & -4
\end{array}\right]
\][/tex]
we will perform the multiplication as follows:
### Step-by-Step Multiplication:
1. First Row:
- Multiply [tex]\(-3\)[/tex] by [tex]\(-2\)[/tex]:
[tex]\[
-3 \times -2 = 6
\][/tex]
- Multiply [tex]\(5\)[/tex] by [tex]\(-2\)[/tex]:
[tex]\[
5 \times -2 = -10
\][/tex]
- Multiply [tex]\(1\)[/tex] by [tex]\(-2\)[/tex]:
[tex]\[
1 \times -2 = -2
\][/tex]
The first row of the resulting matrix is [tex]\([6, -10, -2]\)[/tex].
2. Second Row:
- Multiply [tex]\(8\)[/tex] by [tex]\(-2\)[/tex]:
[tex]\[
8 \times -2 = -16
\][/tex]
- Multiply [tex]\(-2\)[/tex] by [tex]\(-2\)[/tex]:
[tex]\[
-2 \times -2 = 4
\][/tex]
- Multiply [tex]\(3\)[/tex] by [tex]\(-2\)[/tex]:
[tex]\[
3 \times -2 = -6
\][/tex]
The second row of the resulting matrix is [tex]\([-16, 4, -6]\)[/tex].
3. Third Row:
- Multiply [tex]\(2\)[/tex] by [tex]\(-2\)[/tex]:
[tex]\[
2 \times -2 = -4
\][/tex]
- Multiply [tex]\(1\)[/tex] by [tex]\(-2\)[/tex]:
[tex]\[
1 \times -2 = -2
\][/tex]
- Multiply [tex]\(-4\)[/tex] by [tex]\(-2\)[/tex]:
[tex]\[
-4 \times -2 = 8
\][/tex]
The third row of the resulting matrix is [tex]\([-4, -2, 8]\)[/tex].
Putting it all together, we obtain the resulting matrix:
[tex]\[
\left[\begin{array}{ccc}
6 & -10 & -2 \\
-16 & 4 & -6 \\
-4 & -2 & 8
\end{array}\right]
\][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
