4.
$$\mathbf { M } = \left( \begin{array} { l l l }
6 & k & 2
k & 5 & 0
2 & 0 & 7
\end{array} \right)$$
where \(k\) is a constant.
Given that 3 is an eigenvalue of \(\mathbf { M }\),
- determine the possible values of \(k\).
Given that \(k < 0\)
- determine the other eigenvalues of \(\mathbf { M }\).
- Determine a normalised eigenvector corresponding to the eigenvalue 3