Let's solve this step-by-step.
Given the matrix:
[tex]\[
\begin{bmatrix}
-2 & 7 \\
1 & 4
\end{bmatrix}
\][/tex]
and you are required to multiply this matrix by the scalar [tex]\(3\)[/tex].
Step 1: Multiply each element in the matrix by the scalar [tex]\(3\)[/tex].
- For the element in the first row, first column ([tex]\(-2\)[/tex]):
[tex]\[
3 \times -2 = -6
\][/tex]
- For the element in the first row, second column ([tex]\(7\)[/tex]):
[tex]\[
3 \times 7 = 21
\][/tex]
- For the element in the second row, first column ([tex]\(1\)[/tex]):
[tex]\[
3 \times 1 = 3
\][/tex]
- For the element in the second row, second column ([tex]\(4\)[/tex]):
[tex]\[
3 \times 4 = 12
\][/tex]
Step 2: Construct the resulting matrix after the scalar multiplication:
[tex]\[
\begin{bmatrix}
-6 & 21 \\
3 & 12
\end{bmatrix}
\][/tex]
Step 3: Identify the element [tex]\(c_{2,1}\)[/tex] from the resulting matrix. The notation [tex]\(c_{2,1}\)[/tex] refers to the element in the second row, first column of the matrix.
From the resulting matrix:
[tex]\[
\begin{bmatrix}
-6 & 21 \\
3 & 12
\end{bmatrix}
\][/tex]
The element [tex]\(c_{2,1}\)[/tex] is [tex]\(3\)[/tex].
Thus, the product for [tex]\(c_{2,1}\)[/tex] is: [tex]\(3\)[/tex].
So, the correct answer is:
b. 3
