| Exam Board | OCR |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2008 |
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| Session | June |
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| Topic | Proof by induction |
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4 The matrix \(\mathbf { A }\) is given by \(\mathbf { A } = \left( \begin{array} { l l } 3 & 1
0 & 1 \end{array} \right)\). Prove by induction that, for \(n \geqslant 1\),
$$\mathbf { A } ^ { n } = \left( \begin{array} { c c }
3 ^ { n } & \frac { 1 } { 2 } \left( 3 ^ { n } - 1 \right)
0 & 1
\end{array} \right)$$