Respuesta :
Answer:
Explanation:
For the matrix equation
[tex]2X+A=B[/tex]We first subtract A from both sides to get
[tex]2X=B-A_{}[/tex]Now,
[tex]B-A=\begin{bmatrix}{-7} & {-8} & {} \\ {-2} & {6} & {} \\ {4} & {4} & {}\end{bmatrix}-\begin{bmatrix}{-3} & {0} & {} \\ {0} & {3} & {} \\ {-6} & {6} & {}\end{bmatrix}[/tex][tex]B-A=\begin{bmatrix}{-7--3} & {-8-0} & {\square} \\ {-2-0} & {6-3} & {\square} \\ {4--6} & {4-6} & {\square}\end{bmatrix}[/tex][tex]B-A=\begin{bmatrix}{-10} & {-8} & {} \\ {-2} & {-3} & {} \\ {10} & {-2} & {}\end{bmatrix}[/tex]Hence, we have
[tex]2X=\begin{bmatrix}{-10} & {-8} & {} \\ {-2} & {-3} & {} \\ {10} & {-2} & {}\end{bmatrix}[/tex]Dividing both sides by 2 gives
[tex]\begin{gathered} X=\frac{1}{2}\cdot\begin{bmatrix}{-10} & {-8} & {} \\ {-2} & {-3} & {} \\ {10} & {-2} & {}\end{bmatrix} \\ \end{gathered}[/tex][tex]X=\begin{bmatrix}{-5} & {-4} & {} \\ {-1} & {-\frac{3}{2}} & {} \\ {5} & {-1} & {}\end{bmatrix}[/tex]which is our answer!
