6. It is given that \(\left( \begin{array} { l } 1
2
0 \end{array} \right)\) is an eigenvector of the matrix \(\mathbf { A }\), where
$$\mathbf { A } = \left( \begin{array} { l l l }
4 & 2 & 3
2 & b & 0
a & 1 & 8
\end{array} \right)$$
and \(a\) and \(b\) are constants.
- Find the eigenvalue of \(\mathbf { A }\) corresponding to the eigenvector \(\left( \begin{array} { l } 1
2
0 \end{array} \right)\). - Find the values of \(a\) and \(b\).
- Find the other eigenvalues of \(\mathbf { A }\).