2. (a) The matrices \(\mathbf { A }\) and \(\mathbf { B }\) are defined by $$\mathbf { A } = \left( \begin{array} { c c } 3 & 4
- 1 & - 2 \end{array} \right) , \quad \mathbf { B } = \binom { - 11 } { 7 }$$ Given that \(\mathbf { A X } = \mathbf { B }\), find the matrix \(\mathbf { X }\).
(b) (i) Find the \(2 \times 2\) matrix, \(\mathbf { T }\), which represents a reflection in the line \(y = - 2 x\).
(ii) The images of the points \(C ( 2,7 )\) and \(D ( 3,1 )\), under \(\mathbf { T }\), are \(E\) and \(F\) respectively. Find the coordinates of the midpoint of \(E F\).