6 The matrix A, where
$$\mathbf { A } = \left( \begin{array} { r r r }
1 & 0 & 0
10 & - 7 & 10
7 & - 5 & 8
\end{array} \right)$$
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 \(\mathbf { P } ^ { - 1 } \mathbf { A P } = \mathbf { D }\).