3.
$$\mathbf { A } = \left( \begin{array} { l l l }
2 & 1 & 0
1 & 2 & 1
0 & 1 & 2
\end{array} \right)$$
- Find the eigenvalues of \(\mathbf { A }\).
- Find a normalised eigenvector for each of the eigenvalues of \(\mathbf { A }\).
- Write down a matrix \(\mathbf { P }\) and a diagonal matrix \(\mathbf { D }\) such that \(\mathbf { P } ^ { \mathrm { T } } \mathbf { A P } = \mathbf { D }\).