| Exam Board | CAIE |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2019 |
| Session | November |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Invariant lines and eigenvalues and vectors |
8 The matrix $\mathbf { M }$ is defined by
$$\mathbf { M } = \left( \begin{array} { c c c }
2 & m & 1 \\
0 & m & 7 \\
0 & 0 & 1
\end{array} \right) ,$$
where $m \neq 0,1,2$.\\
(i) Find a matrix $\mathbf { P }$ and a diagonal matrix $\mathbf { D }$ such that $\mathbf { M } = \mathbf { P D P } ^ { - 1 }$.\\
(ii) Find $\mathbf { M } ^ { 7 } \mathbf { P }$.\\
\hfill \mbox{\textit{CAIE FP1 2019 Q8}}