10 Find the eigenvalues and corresponding eigenvectors of the matrix \(\mathbf { A }\), where $$\mathbf { A } = \left( \begin{array} { r r r } 6 & 4 & 1
- 6 & - 1 & 3
8 & 8 & 4 \end{array} \right)$$ Hence find a non-singular matrix \(\mathbf { P }\) and a diagonal matrix \(\mathbf { D }\) such that \(\mathbf { A } + \mathbf { A } ^ { 2 } + \mathbf { A } ^ { 3 } = \mathbf { P D P } \mathbf { P } ^ { - 1 }\).