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

Find the solution to the system of equations represented by this matrix equation using-example-1

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Answer:

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}

User Benselme
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