Question

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

Answer 1

Answer:

  D) $\left[\begin{array}{c}\frac{5}{4}\\-\frac{1}{2}\end{array}\right]$

Step-by-step 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: $\dfrac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\end{array}\right]$

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

so the solution is ...

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