Answer
The matrix $ X $ is, $ X=\left[ \begin{matrix}
-2 & -6 \\
3 & \frac{1}{3} \\
\end{matrix} \right]$
Work Step by Step
Consider the given matrix equation $3X+A=B $.
Now put the matrices $ A $ and $ B $ in the above matrix equation and then simplify for $ X $ as below:
$3X+\left[ \begin{matrix}
4 & 6 \\
-5 & 0 \\
\end{matrix} \right]=\left[ \begin{matrix}
-2 & -12 \\
4 & 1 \\
\end{matrix} \right]$
Now subtract the matrix $\left[ \begin{matrix}
4 & 6 \\
-5 & 0 \\
\end{matrix} \right]$ from both sides of the above expression to get, $\begin{align}
& 3X=\left[ \begin{matrix}
-2 & -12 \\
4 & 1 \\
\end{matrix} \right]-\left[ \begin{matrix}
4 & 6 \\
-5 & 0 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-2-4 & -12-6 \\
4+5 & 1-0 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-6 & -18 \\
9 & 1 \\
\end{matrix} \right]
\end{align}$
So, $3X=\left[ \begin{matrix}
-6 & -18 \\
9 & 1 \\
\end{matrix} \right]$
Dividing both sides by 3 we get, $\begin{align}
& X=\frac{1}{3}\left[ \begin{matrix}
-6 & -18 \\
9 & 1 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-2 & -6 \\
3 & \frac{1}{3} \\
\end{matrix} \right]
\end{align}$
Thus, $ X=\left[ \begin{matrix}
-2 & -6 \\
3 & \frac{1}{3} \\
\end{matrix} \right]$
