- The matrix \(\mathbf { M }\) is given by
$$\mathbf { M } = \left( \begin{array} { r r r }
2 & 1 & 0
1 & 2 & 0
- 1 & 0 & 4
\end{array} \right)$$
- Show that 4 is an eigenvalue of \(\mathbf { M }\), and find the other two eigenvalues.
- For each of the eigenvalues find a corresponding eigenvector.
- Find a matrix \(\mathbf { P }\) such that \(\mathbf { P } ^ { - 1 } \mathbf { M P }\) is a diagonal matrix.