CAIE Further Paper 2 2020 Specimen — Question 0

Exam BoardCAIE
ModuleFurther Paper 2 (Further Paper 2)
Year2020
SessionSpecimen
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicInvariant lines and eigenvalues and vectors
DifficultyStandard +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.
Spec4.03h Determinant 2x2: calculation4.03o Inverse 3x3 matrix

0 & 2 & 2
- 1 & 1 & 3 \end{array} \right) .$$
  1. Find the eigenvalues of \(\mathbf { A }\).
  2. Use the characteristic equation of \(\mathbf { A }\) to find \(\mathbf { A } ^ { - 1 }\).

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}}