5 The matrix \(\mathbf { A }\), given by
$$\mathbf { A } = \left( \begin{array} { l l l }
1 & 2 & - 2
6 & 4 & - 6
6 & 5 & - 7
\end{array} \right)$$
has eigenvalues \(1 , - 1\) and - 2 .
- Find a set of corresponding eigenvectors.
- The matrix \(\mathbf { B }\) is given by \(\mathbf { B } = \mathbf { A } - 2 \mathbf { I }\), where \(\mathbf { I }\) is the \(3 \times 3\) identity matrix. Write down the eigenvalues of \(\mathbf { B }\), and state a set of corresponding eigenvectors.