To solve the given problem, we need to perform scalar multiplication on the given matrix.
The matrix provided is:
[tex]\[
\begin{bmatrix}
-2 & -8 & -11 & -5 \\
-11 & -2 & -10 & 7 \\
\end{bmatrix}
\][/tex]
The scalar that we use for multiplication is 8.
When multiplying a matrix by a scalar, each element in the matrix is multiplied by the scalar.
Consider the matrix
[tex]\(
\begin{bmatrix}
a & b & c & d \\
e & f & g & h \\
\end{bmatrix}
\)[/tex]
and the scalar [tex]\( k \)[/tex].
The result of multiplying this matrix by the scalar is:
[tex]\[
k \begin{bmatrix}
a & b & c & d \\
e & f & g & h \\
\end{bmatrix}
=
\begin{bmatrix}
ka & kb & kc & kd \\
ke & kf & kg & kh \\
\end{bmatrix}
\][/tex]
Now in this case, we have:
[tex]\[
8 \begin{bmatrix}
-2 & -8 & -11 & -5 \\
-11 & -2 & -10 & 7 \\
\end{bmatrix}
\][/tex]
Performing the multiplication for each individual element:
1. [tex]\( 8 \times -2 = -16 \)[/tex]
2. [tex]\( 8 \times -8 = -64 \)[/tex]
3. [tex]\( 8 \times -11 = -88 \)[/tex]
4. [tex]\( 8 \times -5 = -40 \)[/tex]
5. [tex]\( 8 \times -11 = -88 \)[/tex]
6. [tex]\( 8 \times -2 = -16 \)[/tex]
7. [tex]\( 8 \times -10 = -80 \)[/tex]
8. [tex]\( 8 \times 7 = 56 \)[/tex]
Thus, the resulting matrix is:
[tex]\[
\begin{bmatrix}
-16 & -64 & -88 & -40 \\
-88 & -16 & -80 & 56 \\
\end{bmatrix}
\][/tex]
So the correct choice is:
A.
[tex]\[
\begin{bmatrix}
-16 & -64 & -88 & -40 \\
-88 & -16 & -80 & 56 \\
\end{bmatrix}
\][/tex]
