- The matrix \(\mathbf { A }\) is given by
$$\mathbf { A } = \left( \begin{array} { r r r }
6 & - 2 & 2
- 2 & 3 & - 1
2 & - 1 & 3
\end{array} \right)$$
- Show that 2 is a repeated eigenvalue of \(\mathbf { A }\) and find the other eigenvalue.
- Hence find three non-parallel eigenvectors of \(\mathbf { A }\).
- Find a matrix \(\mathbf { P }\) such that \(\mathbf { P } ^ { - 1 } \mathbf { A P }\) is a diagonal matrix.