| Exam Board | CAIE |
|---|---|
| Module | Further Paper 2 (Further Paper 2) |
| Year | 2020 |
| Session | Specimen |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Invariant lines and eigenvalues and vectors |
| Difficulty | Standard +0.3 This is a straightforward Further Maths linear algebra question requiring standard techniques: finding eigenvalues via the characteristic polynomial (2×2 matrix makes this routine) and using Cayley-Hamilton theorem to find the inverse. Both parts are textbook procedures with no novel insight required, though slightly above average difficulty due to being Further Maths content. |
| Spec | 4.03h Determinant 2x2: calculation4.03o Inverse 3x3 matrix |
0 & 2 & 2 \\
- 1 & 1 & 3
\end{array} \right) .$$
(i) Find the eigenvalues of $\mathbf { A }$.\\
(ii) Use the characteristic equation of $\mathbf { A }$ to find $\mathbf { A } ^ { - 1 }$.\\
\hfill \mbox{\textit{CAIE Further Paper 2 2020 Q0}}