| Exam Board | AQA |
|---|
| Module | Further Paper 1 (Further Paper 1) |
|---|
| Session | Specimen |
|---|
| Marks | 5 |
|---|
| Topic | Proof by induction |
|---|
13 Given that \(\mathbf { M } = \left[ \begin{array} { l l l } 1 & 1 & 1
1 & 1 & 1
1 & 1 & 1 \end{array} \right]\), prove that \(\mathbf { M } ^ { n } = \left[ \begin{array} { l l l } 3 ^ { n - 1 } & 3 ^ { n - 1 } & 3 ^ { n - 1 }
3 ^ { n - 1 } & 3 ^ { n - 1 } & 3 ^ { n - 1 }
3 ^ { n - 1 } & 3 ^ { n - 1 } & 3 ^ { n - 1 } \end{array} \right]\) for all \(n \in \mathbb { N }\)
[0pt]
[5 marks]
LL
LL
L
LL
LL
LL
L
L