To find the product of the matrix
[tex]\[
\begin{bmatrix}
2 & 3 & 4 \\
9 & -1 & -7 \\
11 & 5 & -3
\end{bmatrix}
\][/tex]
and the scalar multiplier 5, we need to multiply each entry of the matrix by 5.
Let's perform this step-by-step for each element of the matrix:
1. Multiply the element in the first row and first column: [tex]\(5 \times 2 = 10\)[/tex]
2. Multiply the element in the first row and second column: [tex]\(5 \times 3 = 15\)[/tex]
3. Multiply the element in the first row and third column: [tex]\(5 \times 4 = 20\)[/tex]
This completes the first row of our resulting matrix:
[tex]\[
\begin{bmatrix}
10 & 15 & 20 \\
& & \\
& &
\end{bmatrix}
\][/tex]
Next, we proceed to the second row:
4. Multiply the element in the second row and first column: [tex]\(5 \times 9 = 45\)[/tex]
5. Multiply the element in the second row and second column: [tex]\(5 \times (-1) = -5\)[/tex]
6. Multiply the element in the second row and third column: [tex]\(5 \times (-7) = -35\)[/tex]
This completes the second row of our resulting matrix:
[tex]\[
\begin{bmatrix}
10 & 15 & 20 \\
45 & -5 & -35 \\
& &
\end{bmatrix}
\][/tex]
Finally, we proceed to the third row:
7. Multiply the element in the third row and first column: [tex]\(5 \times 11 = 55\)[/tex]
8. Multiply the element in the third row and second column: [tex]\(5 \times 5 = 25\)[/tex]
9. Multiply the element in the third row and third column: [tex]\(5 \times (-3) = -15\)[/tex]
This completes the third row of our resulting matrix:
[tex]\[
\begin{bmatrix}
10 & 15 & 20 \\
45 & -5 & -35 \\
55 & 25 & -15
\end{bmatrix}
\][/tex]
So, the product of the matrix and the scalar 5 is:
[tex]\[
\begin{bmatrix}
10 & 15 & 20 \\
45 & -5 & -35 \\
55 & 25 & -15
\end{bmatrix}
\][/tex]
