Answer:
The value of B-CF is [tex]\begin{bmatrix}23&6.5\\ -6&44\end{bmatrix}[/tex].
Step-by-step explanation:
The given matrices are
[tex]B=\begin{bmatrix}2&8\\ 6&3\end{bmatrix}[/tex]
[tex]C=\begin{bmatrix}12&0&1.5\\ 1&-6&7\end{bmatrix}[/tex]
[tex]F=\begin{bmatrix}-2&0\\ 0&8\\ 2&1\end{bmatrix}[/tex]
We need to find the value of B - CF.
First find the value CF.
[tex]CF=\begin{bmatrix}12&0&1.5\\ 1&-6&7\end{bmatrix}\begin{bmatrix}-2&0\\ 0&8\\ 2&1\end{bmatrix}[/tex]
[tex]CF=\begin{bmatrix}12\left(-2\right)+0\cdot \:0+1.5\cdot \:2&12\cdot \:0+0\cdot \:8+1.5\cdot \:1\\ 1\cdot \left(-2\right)+\left(-6\right)\cdot \:0+7\cdot \:2&1\cdot \:0+\left(-6\right)\cdot \:8+7\cdot \:1\end{bmatrix}[/tex]
[tex]CF=\begin{bmatrix}-21&1.5\\ 12&-41\end{bmatrix}[/tex]
Now, find the value of B - CF.
[tex]B-CF=\begin{bmatrix}2&8\\ 6&3\end{bmatrix}-\begin{bmatrix}-21&1.5\\ 12&-41\end{bmatrix}[/tex]
[tex]B-CF=\begin{bmatrix}23&6.5\\ -6&44\end{bmatrix}[/tex]
Therefore the value of B-CF is [tex]\begin{bmatrix}23&6.5\\ -6&44\end{bmatrix}[/tex].
