The matrix A, where
\(\mathbf{A}=\left(\begin{array}{rrr} 1 & 0 & 0 \\ 10 & -7 & 10 \\ 7 & -5 & 8 \end{array}\right),\)
has eigenvalues 1 and 3 . Find corresponding eigenvectors.

It is given that \(\left(\begin{array}{l}0 \\ 2 \\ 1\end{array}\right)\) is an eigenvector of \(\mathbf{A}\). Find the corresponding eigenvalue.

Find a diagonal matrix \(\mathbf{D}\) and matrices \(\mathbf{P}\) and \(\mathbf{P}^{-1}\) such that \(\mathbf{P}^{-1} \mathbf{A P}=\mathbf{D}\).