CAIE A-Level Further Math AS 1.4.2 Determinants and Inverses Questions

Practise calculating determinants, testing singularity and finding inverse matrices.

Exam points

calculate determinants and test singularity
find inverse matrices and matrix powers
solve determinant and inverse problems in context

[Maximum number: 2]

Let $\mathbf{A}=\left(\begin{array}{ll}3 & 0 \\ 1 & 1\end{array}\right)$ .

Find, in terms of n, the inverse of $\mathbf{A}^{n}$ .

$\operatorname{det} \mathbf{A}^{n}=\operatorname{det}\left(\begin{array}{cc}3^{n} & 0 \frac{1}{2}\left(3^{n}-1\right) & 1\end{array}\right)=3^{n}$

Or a multiple of $\mathbf{A}^{-n}=2^{-1} 3^{-n}\left(\begin{array}{cc}2 & 0 1-3^{n} & 2 \times 3^{n}\end{array}\right)$ seen.
$\mathbf{A}^{-n}=3^{-n}\left(\begin{array}{cc}1 \frac{1}{2}\left(1-3^{n}\right) 3^{n}\end{array}\right)$
OE $\mathbf{A}^{-n}=2^{-1} 3^{-n}\left(\begin{array}{cc}2 1-3^{n} 2 \times 3^{n}\end{array}\right)$

2

All question bank results loaded

CAIE A-Level Further Math AS 1.4.2 Determinants and Inverses Questions question 1