Question

Find the solution to the system of equations represented by this matrix equation using an inverse matrix.

Answer 1

D)
`\left[\begin{array}{c}(5)/(4)\\-(1)/(2)\end{array}\right]`

Explanation:

For matrix
`\left[\begin{array}{cc}a&b\\c&d\end{array}\right]`

the inverse matrix is the transpose of the cofactor matrix, divided by the determinant:
`(1)/(ad-bc)\left[\begin{array}{cc}d&-b\\-c&a\end{array}\right]`

Your inverse matrix is:
`(1)/(2(-3)-(1)(2))\left[\begin{array}{cc}-3&-1\\-2&2\end{array}\right]`

so the solution is ...

`\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{cc}(3)/(8)&(1)/(8)\\(1)/(4)&-(1)/(4)\end{array}\right] \cdot\left[\begin{array}{c}2\\4\end{array}\right] =\left[\begin{array}{c}(5)/(4)\\-(1)/(2)\end{array}\right] \qquad\text{matches selection D}`