2. The rectangle \(R\) has vertices at the points \(( 0,0 ) , ( 1,0 ) , ( 1,2 )\) and \(( 0,2 )\).
- Find the coordinates of the vertices of the image of \(R\) under the transformation given by the matrix \(\mathbf { A } = \left( \begin{array} { c c } a & 4
- 1 & 1 \end{array} \right)\), where \(a\) is a constant. - Find det \(\mathbf { A }\), giving your answer in terms of \(a\).
Given that the area of the image of \(R\) is 18 ,
- find the value of \(a\).