Answer:
[tex]3B-4C=\begin{pmatrix}-8&-23\\ 1&-15\end{pmatrix}[/tex]
Step-by-step explanation:
Let
[tex]B=\begin{pmatrix}8&-5\\ -1&3\end{pmatrix}[/tex]
and
[tex]C=\begin{pmatrix}8&2\\ \:-1&6\end{pmatrix}\:[/tex]
Finding 3B-4C
[tex]\:3B-4C\:=\:3\begin{pmatrix}8&-5\\ -1&3\end{pmatrix}\:-4\begin{pmatrix}8&2\\ \:-1&6\end{pmatrix}[/tex]
first solving
[tex]3\begin{pmatrix}8&-5\\ -1&3\end{pmatrix}[/tex]
Scalar multiplication: Multiply each of the matrix elements by a scalar
[tex]3\begin{pmatrix}8&-5\\ \:\:-1&3\end{pmatrix}=\begin{pmatrix}3\cdot \:\:8&3\left(-5\right)\\ \:3\left(-1\right)&3\cdot \:\:3\end{pmatrix}[/tex]
simplify each element
[tex]=\begin{pmatrix}24&-15\\ -3&9\end{pmatrix}[/tex]
now solving
[tex]4\begin{pmatrix}8&2\\ \:\:-1&6\end{pmatrix}[/tex]
Scalar multiplication: Multiply each of the matrix elements by a scalar
[tex]4\begin{pmatrix}8&2\\ \:\:-1&6\end{pmatrix}=\begin{pmatrix}4\cdot \:\:8&4\cdot \:\:2\\ \:4\left(-1\right)&4\cdot \:\:6\end{pmatrix}[/tex]
simplify each element
[tex]=\begin{pmatrix}32&8\\ -4&24\end{pmatrix}[/tex]
now combining the results
[tex]\:3B-4C\:=\:3\begin{pmatrix}8&-5\\ -1&3\end{pmatrix}\:-4\begin{pmatrix}8&2\\ \:-1&6\end{pmatrix}[/tex]
[tex]=\begin{pmatrix}24&-15\\ -3&9\end{pmatrix}-\begin{pmatrix}32&8\\ -4&24\end{pmatrix}[/tex]
subtract the elements in the matching positions
[tex]=\begin{pmatrix}24-32&\left(-15\right)-8\\ \left(-3\right)-\left(-4\right)&9-24\end{pmatrix}[/tex]
simplifying the elements
[tex]=\begin{pmatrix}-8&-23\\ 1&-15\end{pmatrix}[/tex]
Therefore,
[tex]3B-4C=\begin{pmatrix}-8&-23\\ 1&-15\end{pmatrix}[/tex]
