8.
$$\mathbf { A } = \left( \begin{array} { r r }
2 & - 2
- 1 & 3
\end{array} \right)$$
- Find \(\operatorname { det } \mathbf { A }\).
- Find \(\mathbf { A } ^ { - 1 }\).
The triangle \(R\) is transformed to the triangle \(S\) by the matrix \(\mathbf { A }\). Given that the area of triangle \(S\) is 72 square units,
- find the area of triangle \(R\).
The triangle \(S\) has vertices at the points \(( 0,4 ) , ( 8,16 )\) and \(( 12,4 )\).
- Find the coordinates of the vertices of \(R\).