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UK A Level Further Mathematics · independent study
Independent myAudience subject study using references for England. Published readings cover selected topics; full curriculum, assessment and practical coverage are not verified. No awarding-body affiliation, endorsement, qualification or grade guarantee is offered. Check the source specification and your centre for the requirements of your chosen course.
Why an induction proof reaches every integer
Induction when multiplication has an order
Complex arithmetic and the real-coefficient condition
Arguments, quadrants and geometric conditions
Powers, roots and regular polygons
Composition order and fixed geometry
![Matrix A=[[2,1],[1,1]] maps basis vectors to (2,1) and (1,1), forming a determinant-one parallelogram. Singular B=[[1,3],[2,6]] maps onto y=2x; (4,8) is reachable with infinitely many inputs and (4,9) is not. Separate axes are illustrative, not a physical equal-scale measurement.](/assets/lesson-further-maths-determinant-inverse-v1.webp)
Area, orientation and when inversion fails
Three planes: a point, a line or no meeting