Certainly! Let's multiply the scalar [tex]\(-\frac{1}{5}\)[/tex] with the given matrix [tex]\(\begin{bmatrix} -5 \\ 11 \end{bmatrix}\)[/tex].
### Step-by-Step Solution:
1. Identify the Scalar and the Matrix:
- Scalar: [tex]\( -\frac{1}{5} \)[/tex]
- Matrix: [tex]\(\begin{bmatrix} -5 \\ 11 \end{bmatrix}\)[/tex]
2. Multiply the Scalar with Each Element of the Matrix:
We will multiply each entry in the matrix by the scalar [tex]\( -\frac{1}{5} \)[/tex]:
- First row: [tex]\( -\frac{1}{5} \times (-5) = 1 \)[/tex]
- Second row: [tex]\( -\frac{1}{5} \times 11 = -2.2 \)[/tex]
3. Form the Resulting Matrix:
After performing the multiplication, we get the resulting matrix as:
[tex]\[
\begin{bmatrix}
1 \\
-2.2
\end{bmatrix}
\][/tex]
### Conclusion:
The product of [tex]\(-\frac{1}{5}\)[/tex] and the matrix [tex]\(\begin{bmatrix} -5 \\ 11 \end{bmatrix}\)[/tex] is [tex]\(\begin{bmatrix} 1 \\ -2.2 \end{bmatrix}\)[/tex].
