Question

Select the best answer for the question

Answer 1

Answer:

C. $\left[\begin{array}{ccc}-24&0&-3\\8&-48&56\\25&-6&10\end{array}\right]$

Step-by-step explanation:

The given matrices are;

$F=\left[\begin{array}{cc}-2&0\\0&8\\2&1\end{array}\right]$

and

$C=\left[\begin{array}{ccc}12&0&\frac{3}{2}\\1&-6&7\end{array}\right]$

$FC=\left[\begin{array}{cc}-2&0\\0&8\\2&1\end{array}\right]\left[\begin{array}{ccc}12&0&\frac{3}{2}\\1&-6&7\end{array}\right]$

$FC=\left[\begin{array}{ccc}12(-2)+0(1)&0(-2)+-6(0)&\frac{3}{2}(-2)+7(0)\\12(0)+8(1)&0(0)+8(-6)&0(\frac{3}{2})+8(7)\\2(12)+1(1)&2(0)+1(-6)&2(\frac{3}{2})+1(7)\end{array}\right]$

This simplifies to;

$FC=\left[\begin{array}{ccc}-24&0&-3\\8&-48&56\\25&-6&10\end{array}\right]$

The correct answer is C