| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2011 |
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| Session | June |
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| Topic | Proof by induction |
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2 Let \(\mathbf { A } = \left( \begin{array} { l l } 2 & 3
0 & 1 \end{array} \right)\). Prove by mathematical induction that, for every positive integer \(n\),
$$\mathbf { A } ^ { n } = \left( \begin{array} { c c }
2 ^ { n } & 3 \left( 2 ^ { n } - 1 \right)
0 & 1
\end{array} \right)$$