3.
$$\mathbf { M } = \left( \begin{array} { r r }
- 2 & 5
6 & k
\end{array} \right)$$
where \(k\) is a constant.
Given that
$$\mathbf { M } ^ { 2 } + 11 \mathbf { M } = a \mathbf { I }$$
where \(a\) is a constant and \(\mathbf { I }\) is the \(2 \times 2\) identity matrix,
- determine the value of \(a\)
- show that \(k = - 9\)
- Determine the equations of the invariant lines of the transformation represented by \(\mathbf { M }\).
- State which, if any, of the lines identified in (b) consist of fixed points, giving a reason for your answer.