Answer
$X=\begin{bmatrix}-2&-6\\3&\frac{1}{3}\end{bmatrix}$
Work Step by Step
We are given the equation:
$3X+A=B$, $A=\begin{bmatrix}4&6\\-5&0\end{bmatrix}$, $B=\begin{bmatrix}-2&-12\\4&1\end{bmatrix}$
We have:
$3X=B-A$
$X=\dfrac{1}{3}(B-A)=\dfrac{1}{3}\left(\begin{bmatrix}-2&-12\\4&1\end{bmatrix}-\begin{bmatrix}4&6\\-5&0\end{bmatrix}\right)$
$=\dfrac{1}{3}\left(\begin{bmatrix}-2-4&-12-6\\4-(-5)&1-0\end{bmatrix}\right)$
$=\dfrac{1}{3}\left(\begin{bmatrix}-6&-18\\9&1\end{bmatrix}\right)$
$=\begin{bmatrix}-2&-6\\3&\frac{1}{3}\end{bmatrix}$
We got:
$X=\begin{bmatrix}-2&-6\\3&\frac{1}{3}\end{bmatrix}$
