5.
$$\mathbf { M } = \left( \begin{array} { r r r }
6 & - 2 & - 1
- 2 & 6 & - 1
- 1 & - 1 & 5
\end{array} \right)$$
Given that 8 is an eigenvalue of \(\mathbf { M }\)
- determine an eigenvector corresponding to the eigenvalue 8
- Determine the other two eigenvalues of \(\mathbf { M }\).
- Hence find an orthogonal matrix \(\mathbf { P }\) and a diagonal matrix \(\mathbf { D }\) such that \(\mathbf { P } ^ { T } \mathbf { M P } = \mathbf { D }\)
5.