Option C:
[tex]\left(\begin{array}{cc}-6 & 0 \\12 & 21\end{array}\right)[/tex]
Solution:
Given data:
[tex]3\left[\begin{array}{cc}-2 & 0 \\4 & 7\end{array}\right][/tex]
To find the product:
Scalar element = 3
Scalar multiplication:
Multiply each of the matrix element by a scalar.
Here multiply each of the matrix element by 3.
[tex]3\left(\begin{array}{cc}-2 & 0 \\4 & 7\end{array}\right)=\left(\begin{array}{ccc}3(-2) & 3 \cdot 0 \\3 \cdot 4 & 3 \cdot 7\end{array}\right)[/tex]
Simplifying each element, we get
[tex]=\left(\begin{array}{cc}-6 & 0 \\12 & 21\end{array}\right)[/tex]
The value of the given matrix is [tex]\left(\begin{array}{cc}-6 & 0 \\12 & 21\end{array}\right)[/tex].
Option C is the correct answer.
