| Exam Board | CAIE |
|---|
| Module | FP1 (Further Pure Mathematics 1) |
|---|
| Year | 2012 |
|---|
| Session | June |
|---|
| Topic | 3x3 Matrices |
|---|
5 A matrix \(\mathbf { A }\) has eigenvalues \(- 1,1\) and 2 , with corresponding eigenvectors
$$\left( \begin{array} { r }
0
1
- 2
\end{array} \right) , \quad \left( \begin{array} { r }
- 1
- 1
3
\end{array} \right) \quad \text { and } \quad \left( \begin{array} { r }
2
- 3
5
\end{array} \right) ,$$
respectively. Find \(\mathbf { A }\).