| Exam Board | CAIE |
|---|
| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2010 |
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| Session | November |
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| Topic | 3x3 Matrices |
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9 Find the eigenvalues and corresponding eigenvectors of the matrix
$$\mathbf { A } = \left( \begin{array} { r r r }
3 & - 1 & 0
- 1 & 2 & - 1
0 & - 1 & 3
\end{array} \right)$$
Find a non-singular matrix \(\mathbf { M }\) and a diagonal matrix \(\mathbf { D }\) such that \(( \mathbf { A } - 2 \mathbf { I } ) ^ { 3 } = \mathbf { M D M } ^ { - 1 }\), where \(\mathbf { I }\) is the \(3 \times 3\) identity matrix.