9 The matrix \(\mathbf { M }\), where $$\mathbf { M } = \left( \begin{array} { r r r } - 2 & 2 & 2
2 & 1 & 2
- 3 & - 6 & - 7 \end{array} \right)$$ has an eigenvector \(\left( \begin{array} { r } 0
1
- 1 \end{array} \right)\). Find the corresponding eigenvalue. It is given that if the eigenvalues of a general \(3 \times 3\) matrix \(\mathbf { A }\), where $$\mathbf { A } = \left( \begin{array} { l l l } a & b & c
d & e & f
g & h & i \end{array} \right)$$ are \(\lambda _ { 1 } , \lambda _ { 2 }\) and \(\lambda _ { 3 }\) then $$\lambda _ { 1 } + \lambda _ { 2 } + \lambda _ { 3 } = a + e + i$$ and the determinant of \(\mathbf { A }\) has the value \(\lambda _ { 1 } \lambda _ { 2 } \lambda _ { 3 }\). Use these results to find the other two eigenvalues of the matrix \(\mathbf { M }\), and find corresponding eigenvectors.