- (i) \(\mathbf { A } = \left( \begin{array} { c c } - 3 & 8
- 3 & k \end{array} \right) \quad\) where \(k\) is a constant The transformation represented by \(\mathbf { A }\) transforms triangle \(T\) to triangle \(T ^ { \prime }\) The area of triangle \(T ^ { \prime }\) is three times the area of triangle \(T\)
Determine the possible values of \(k\)
(ii) \(\mathbf { B } = \left( \begin{array} { r r } a & - 4
2 & 3 \end{array} \right)\) and \(\mathbf { B C } = \left( \begin{array} { l l l } 2 & 5 & 1
1 & 4 & 2 \end{array} \right)\) where \(a\) is a constant Determine, in terms of \(a\), the matrix \(\mathbf { C }\)