Given:
[tex]C=\begin{bmatrix}{12} & {0} & {\frac{3}{2}} \\ {1} & {-6} & {7}\end{bmatrix}[/tex]
To find 4C:
Multiplying 4 on both sides we get,
[tex]\begin{gathered} 4C=4\times\begin{bmatrix}{12} & {0} & {\frac{3}{2}} \\ {1} & {-6} & {7}\end{bmatrix} \\ =\begin{bmatrix}{4\times12} & {4\times0} & {4\times\frac{3}{2}} \\ {4\times1} & {4\times(-6)} & {4\times7}\end{bmatrix} \\ =\begin{bmatrix}{48} & {0} & {6} \\ {4} & {-24} & {28}\end{bmatrix} \end{gathered}[/tex]
Hence, the answer is,
[tex]4C=\begin{bmatrix}{48} & {0} & {6} \\ {4} & {-24} & {28}\end{bmatrix}[/tex]
Therefore, the correct option is A.
