| Exam Board | SPS |
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| Module | SPS ASFM (SPS ASFM) |
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| Year | 2020 |
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| Session | May |
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| Topic | Proof by induction |
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6.
In this question you must show detailed reasoning.
\(\mathbf { M }\) is the matrix \(\left( \begin{array} { l l } 1 & 6
0 & 2 \end{array} \right)\).
Prove that \(\mathbf { M } ^ { n } = \left( \begin{array} { c c } 1 & 3 \left( 2 ^ { n + 1 } - 2 \right)
0 & 2 ^ { n } \end{array} \right)\), for any positive integer \(n\).