Answer :
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]
[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]