Question

What is FC?

Answer 1

Answer:

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

Step-by-step explanation:

We have:

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

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

And we need to find FC, this means that we have to find the product between this two matrices.

This product will be possible only if the number of columns of the first matrix is equal to the number of rows of the second matrix.

F is a 3x2 matrix, this means F has 3 rows and 2 columns.

C is a 2x3 matrix this means it has 2 rows and 3 columns.

Then the product is possible because the number of columns of F is equal to the number of rows of C.

And the  resulting matrix will be a 3x3.

By definition the product between two matrices is:

Let's suppose both matrices are 2x2,

$A=\left[\begin{array}{cc}a_{11} &a_{12} \\a_{21} &a_{22}\end{array}\right]$

$B=\left[\begin{array}{cc}b_{11} &b_{12} \\b_{21} &b_{22}\end{array}\right]$

The product between A and B is:

$AB=\left[\begin{array}{cc}a_{11}b_{11}+a_{12}b_{21}&a_{11}b_{12}+a_{12}b_{22}\\a_{21}b_{11}+a_{22}b_{21}&a_{21}b_{12}+a_{22}b_{22}\end{array}\right]$

IMPORTANT: It's not the same AB then BA the results of both products are differents.

Now, doing the product between F and C:

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

$=\left[\begin{array}{ccc}(-2).12+0.1&(-2).0+0.(-6)&(-2).\frac{3}{2} +0.7\\0.12+8.1&0.0+8.(-6)&0.\frac{3}{2} +8.7\\2.12+1.1&2.0+1.(-6)&2.\frac{3}{2} +1.7\end{array}\right] \\ =\left[\begin{array}{ccc}-24&0&-3\\8&-48&56\\25&-6&10\end{array}\right]$

And then the answer is option D.

Answer 2

The answer to this question is
D.