Answer:
x = 3
Inverse matrix:
[tex]A^{-1} = \begin{pmatrix} \frac{1}{9} & \frac{2}{9} \\ \frac{1}{3} & -\frac{1}{3} \end{pmatrix} \quad[/tex]
Step-by-step explanation:
Determinant: ad - bc
a = 3, b = 2, c = 3, d = -1
3 * (-1) - (2 * x) = -9
-3 - 2x = -9
-2x = -6
x = 3
For matrix
[tex]A = \begin{pmatrix}a & b\\c & d\end{pmatrix} \quad[/tex]
the inverse is
[tex]A^{-1} = \dfrac{1}{ad - bc}\begin{pmatrix}d & -b \\-c & a\end{pmatrix}\quad[/tex]
Here we have: det = -9
a = 3, b = 2, c = 3, d = -1
Inverse matrix:
[tex]A^{-1} = \dfrac{1}{-9}\begin{pmatrix} -1 & -2 \\ -3 & 3 \end{pmatrix}\quad[/tex]
[tex]A^{-1} = \begin{pmatrix} \frac{-1}{-9} & \frac{-2}{-9} \\\frac{-3}{-9} & \frac{3}{-9}\end{pmatrix} \quad[/tex]
[tex]A^{-1} = \begin{pmatrix} \frac{1}{9} & \frac{2}{9} \\\frac{1}{3} & -\frac{1}{3}\end{pmatrix}\quad[/tex]
