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 .\\
(i) Find a set of corresponding eigenvectors.\\

(ii) 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.\\

\hfill \mbox{\textit{CAIE FP1 2017 Q5}}