To obtain the product of the scalar [tex]\(-4\)[/tex] and the vector [tex]\(\left[\begin{array}{c} 8 \\ -1 \\ -5 \\ 9 \end{array}\right]\)[/tex], follow these steps:
1. Multiply [tex]\(-4\)[/tex] by each component of the vector individually.
2. Calculate each component separately:
- The first component: [tex]\(-4 \cdot 8 = -32\)[/tex]
- The second component: [tex]\(-4 \cdot -1 = 4\)[/tex]
- The third component: [tex]\(-4 \cdot -5 = 20\)[/tex]
- The fourth component: [tex]\(-4 \cdot 9 = -36\)[/tex]
3. Combine the results to form the resulting vector:
[tex]\[
\left[\begin{array}{c}
-32 \\
4 \\
20 \\
-36
\end{array}\right]
\][/tex]
So, the product of [tex]\(-4\)[/tex] and [tex]\(\left[\begin{array}{c} 8 \\ -1 \\ -5 \\ 9 \end{array}\right]\)[/tex] is
[tex]\[
\left[\begin{array}{c}
-32 \\
4 \\
20 \\
-36
\end{array}\right]
\][/tex]
