| Exam Board | OCR |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2013 |
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| Session | June |
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| Topic | Proof by induction |
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4 The matrix \(\mathbf { M }\) is given by \(\mathbf { M } = \left( \begin{array} { l l } 2 & 2
0 & 1 \end{array} \right)\). Prove by induction that, for \(n \geqslant 1\),
$$\mathbf { M } ^ { n } = \left( \begin{array} { c c }
2 ^ { n } & 2 ^ { n + 1 } - 2
0 & 1
\end{array} \right) .$$