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The eigenvalues of the matrix are: \[ \begin{aligned} \lambda_{1} &= -1 \end{aligned} \] \(\lambda_{1}\) has multiplicity 3. All other eigenvalues have multiplicity 1.
The eigenvectors \(\begin{bmatrix}\frac{6}{7}\\1\\0\end{bmatrix} \approx \begin{bmatrix}0.857142857142857\\1\\0\end{bmatrix} \) , \(\begin{bmatrix}- \frac{5}{7}\\0\\1\end{bmatrix} \approx \begin{bmatrix}-0.714285714285714\\0\\1\end{bmatrix} \) are associated with the eigenvalue \(\lambda_{1}\).