Question

Picture to the problem sented

Answer 1

Explanation:

For the matrix equation

`2X+A=B`

We first subtract A from both sides to get

`2X=B-A_{}`

Now,

`B-A=\begin{bmatrix}{-7} & {-8} & {} \\ {-2} & {6} & {} \\ {4} & {4} & {}\end{bmatrix}-\begin{bmatrix}{-3} & {0} & {} \\ {0} & {3} & {} \\ {-6} & {6} & {}\end{bmatrix}`
`B-A=\begin{bmatrix}{-7--3} & {-8-0} & {\square} \\ {-2-0} & {6-3} & {\square} \\ {4--6} & {4-6} & {\square}\end{bmatrix}`
`B-A=\begin{bmatrix}{-10} & {-8} & {} \\ {-2} & {-3} & {} \\ {10} & {-2} & {}\end{bmatrix}`

Hence, we have

`2X=\begin{bmatrix}{-10} & {-8} & {} \\ {-2} & {-3} & {} \\ {10} & {-2} & {}\end{bmatrix}`

Dividing both sides by 2 gives

`\begin{gathered} X=(1)/(2)\cdot\begin{bmatrix}{-10} & {-8} & {} \\ {-2} & {-3} & {} \\ {10} & {-2} & {}\end{bmatrix} \\ \end{gathered}`
`X=\begin{bmatrix}{-5} & {-4} & {} \\ {-1} & {-(3)/(2)} & {} \\ {5} & {-1} & {}\end{bmatrix}`

which is our answer!