9.
$$\mathbf { M } = \left( \begin{array} { r r }
3 & 4
2 & - 5
\end{array} \right)$$
- Find \(\operatorname { det } \mathbf { M }\).
The transformation represented by \(\mathbf { M }\) maps the point \(S ( 2 a - 7 , a - 1 )\), where \(a\) is a constant, onto the point \(S ^ { \prime } ( 25 , - 14 )\).
- Find the value of \(a\).
The point \(R\) has coordinates \(( 6,0 )\).
Given that \(O\) is the origin,
- find the area of triangle \(O R S\).
Triangle \(O R S\) is mapped onto triangle \(O R ^ { \prime } S ^ { \prime }\) by the transformation represented by \(\mathbf { M }\).
- Find the area of triangle \(O R ^ { \prime } S ^ { \prime }\).
Given that
$$\mathbf { A } = \left( \begin{array} { r r }
0 & - 1
1 & 0
\end{array} \right)$$ - describe fully the single geometrical transformation represented by \(\mathbf { A }\).
The transformation represented by \(\mathbf { A }\) followed by the transformation represented by \(\mathbf { B }\) is equivalent to the transformation represented by \(\mathbf { M }\).
- Find B.