Edexcel A-Level Mathematics AS Fp1 5 5 Inverse of 2 2 Matrices Questions

Practise finding inverses of 2 x 2 matrices, simplifying entries in terms of constants, and using inverse product rules.

Exam points

form A^-1 from the determinant and adjugate, simplifying entries in terms of a or k
apply (AB)^-1 = B^-1A^-1 when finding the inverse of a product matrix
use a matrix equation involving A^-1 or I to solve for an unknown constant

[Maximum number: 2]

$\mathbf M=\left(\text{row }1:2k+1,\ k;\ \text{row }2:k+7,\ k+4\right),$
where k is a constant.

Determine $\mathbf{M}^{-1}$ in terms of k.

The determinant is $k^2+2k+4$ .

$\mathbf M^{-1} =\frac{1}{k^2+2k+4} \left(\text{row }1: k+4,\ -k;\ \text{row }2: -k-7,\ 2k+1\right).$

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