4 The matrices \(\mathbf { A } , \mathbf { B }\) and \(\mathbf { C }\) are given by
$$\mathbf { A } = \left( \begin{array} { c c c }
2 & k & k
5 & - 1 & 3
1 & 0 & 1
\end{array} \right) , \quad \mathbf { B } = \left( \begin{array} { c c }
1 & 0
0 & 1
1 & 0
\end{array} \right) \text { and } \quad \mathbf { C } = \left( \begin{array} { r c c }
0 & 1 & 1
- 1 & 2 & 0
\end{array} \right)$$
where \(k\) is a real constant.
- Find \(\mathbf { C A B }\).
- Given that \(\mathbf { A }\) is singular, find the value of \(k\).
- Using the value of \(k\) from part (b), find the equations of the invariant lines, through the origin, of the transformation in the \(x - y\) plane represented by \(\mathbf { C A B }\).