Answer:
We conclude that:
[tex]3\cdot \:2\begin{pmatrix}-2&3&0\\ -4&2&6\\ 6&-5&6\end{pmatrix}=\begin{pmatrix}-12&18&0\\ -24&12&36\\ 36&-30&36\end{pmatrix}[/tex]
Hence, option B is correct.
Step-by-step explanation:
Given the expression
[tex]3\times 2\begin{pmatrix}-2&3&0\\ \:-4&2&6\\ \:6&-5&6\end{pmatrix}[/tex]
solving
[tex]3\times 2\begin{pmatrix}-2&3&0\\ \:-4&2&6\\ \:6&-5&6\end{pmatrix}[/tex]
Scalar Multiplication: Multiply each of the matrix elements by a scalar
[tex]=\begin{pmatrix}3\cdot \:2\left(-2\right)&3\cdot \:2\cdot \:3&3\cdot \:2\cdot \:0\\ 3\cdot \:2\left(-4\right)&3\cdot \:2\cdot \:2&3\cdot \:2\cdot \:6\\ 3\cdot \:2\cdot \:6&3\cdot \:2\left(-5\right)&3\cdot \:2\cdot \:6\end{pmatrix}[/tex]
Simplify each element
[tex]=\begin{pmatrix}-12&18&0\\ -24&12&36\\ 36&-30&36\end{pmatrix}[/tex]
Therefore, we conclude that:
[tex]3\cdot \:2\begin{pmatrix}-2&3&0\\ -4&2&6\\ 6&-5&6\end{pmatrix}=\begin{pmatrix}-12&18&0\\ -24&12&36\\ 36&-30&36\end{pmatrix}[/tex]
Hence, option B is correct.
