| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2010 |
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| Session | June |
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| Topic | Invariant lines and eigenvalues and vectors |
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1 Given that 5 is an eigenvalue of the matrix
$$\mathbf { A } = \left( \begin{array} { r r r }
5 & - 3 & 0
1 & 2 & 1
- 1 & 3 & 4
\end{array} \right)$$
find a corresponding eigenvector.
Hence find an eigenvalue and a corresponding eigenvector of the matrix \(\mathbf { A } + \mathbf { A } ^ { 2 }\).