Answer:
C. [tex]\left[\begin{array}{ccc}-24&0&-3\\8&-48&56\\25&-6&10\end{array}\right][/tex]
Step-by-step explanation:
The given matrices are;
[tex]F=\left[\begin{array}{cc}-2&0\\0&8\\2&1\end{array}\right][/tex]
and
[tex]C=\left[\begin{array}{ccc}12&0&\frac{3}{2}\\1&-6&7\end{array}\right][/tex]
[tex]FC=\left[\begin{array}{cc}-2&0\\0&8\\2&1\end{array}\right]\left[\begin{array}{ccc}12&0&\frac{3}{2}\\1&-6&7\end{array}\right][/tex]
[tex]FC=\left[\begin{array}{ccc}12(-2)+0(1)&0(-2)+-6(0)&\frac{3}{2}(-2)+7(0)\\12(0)+8(1)&0(0)+8(-6)&0(\frac{3}{2})+8(7)\\2(12)+1(1)&2(0)+1(-6)&2(\frac{3}{2})+1(7)\end{array}\right][/tex]
This simplifies to;
[tex]FC=\left[\begin{array}{ccc}-24&0&-3\\8&-48&56\\25&-6&10\end{array}\right][/tex]
The correct answer is C
