2.
$$\mathbf { A } = \left( \begin{array} { l l }
3 & 2
2 & 6
\end{array} \right)$$
- Find the eigenvalues and corresponding normalised eigenvectors of the matrix \(\mathbf { A }\).
- Write down a matrix \(\mathbf { P }\) and a diagonal matrix \(\mathbf { D }\) such that \(\mathbf { P } ^ { \mathrm { T } } \mathbf { A P } = \mathbf { D }\).