AQA
Further AS Paper 1
Specimen
— Question 4
8 marks
Exam Board
AQA
Module
Further AS Paper 1 (Further AS Paper 1)
Session
Specimen
Marks
8
Topic
Matrices
4
Find the value of \(k\) for which matrix \(\mathbf { A }\) is singular.
4
Describe the transformation represented by matrix \(\mathbf { B }\).
4
Given that \(\mathbf { A }\) and \(\mathbf { B }\) are both non-singular, verify that \(\mathbf { A } ^ { \mathbf { - 1 } } \mathbf { B } ^ { \mathbf { - 1 } } = ( \mathbf { B A } ) ^ { \mathbf { - 1 } }\). [0pt]
[4 marks]
4
(ii) Prove the result \(\mathbf { M } ^ { - \mathbf { 1 } } \mathbf { N } ^ { - \mathbf { 1 } } = ( \mathbf { N M } ) ^ { - \mathbf { 1 } }\) for all non-singular square matrices \(\mathbf { M }\) and \(\mathbf { N }\) of the same size. [0pt]
[4 marks]