Question

Given the matrices A and B shown below, solve for X in the equation- {A + }X = B.А.|10-12AB=1074712Rows: 2Columns: 2Submit Answerattemption

Answer 1

We will solve for X in the matrix equation first,

`\begin{gathered} -(1)/(2)A+(1)/(3)X=B \\ (1)/(3)X=B+(1)/(2)A \\ X=(B+(1)/(2)A)/((1)/(3)) \\ X=3*(B+(1)/(2)A) \end{gathered}`

We calculate (1/2 A) first and add it to B.

Then, multiply that matrix by the scalar constant "3".

The process is shown below:

`\begin{gathered} X=3*(B+(1)/(2)A) \\ X=3*(\begin{bmatrix}-10 & 7 \\ 7 & 12\end{bmatrix}+(1)/(2)\begin{bmatrix}10 & -4 \\ -12 & 4\end{bmatrix}) \\ X=3*(\begin{bmatrix}-10 & 7 \\ 7 & 12\end{bmatrix}+\begin{bmatrix}5 & -2 \\ -6 & 2\end{bmatrix}) \\ X=3*\begin{bmatrix}-10+5 & 7-2 \\ 7-6 & 12+2\end{bmatrix} \\ X=3*\begin{bmatrix}-5 & 5 \\ 1 & 14\end{bmatrix} \\ X=\begin{bmatrix}-15 & 15 \\ 3 & 42\end{bmatrix} \end{gathered}`