| Exam Board | AQA |
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| Module | Further Paper 1 (Further Paper 1) |
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| Year | 2021 |
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| Session | June |
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| Marks | 5 |
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| Topic | Proof by induction |
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5 The matrix \(\mathbf { M }\) is defined by \(\mathbf { M } = \left[ \begin{array} { c c c } 3 & 2 & - 2
0 & 1 & 0
0 & 0 & 1 \end{array} \right]\)
Prove by induction that \(\mathbf { M } ^ { n } = \left[ \begin{array} { c c c } 3 ^ { n } & 3 ^ { n } - 1 & - 3 ^ { n } + 1
0 & 1 & 0
0 & 0 & 1 \end{array} \right]\) for all integers \(n \geq 1\) [5 marks]