Chapter 14: Further Pure 2: Matrix Algebra

A-level Further MathsFurther Pure 1 & 23 topicsHigher

StudyStudy Material QuizQuiz ResourcesResources

Mock Papers

Exam-board mock papers

Mock papers launch from 1 August 2026. New papers will be added regularly from this date.

Dashboard tracking

Included with paid subject access

You can see the paper details now. Access unlocks when your plan includes this subject and tier.

Mock paperFeatured

Mock papers launch collection

alevel · further-maths · Further Pure 1 & 2 · All papers

Releases 1 August 2026

Locked

Topic-aware long answers

Ultimate/Lifetime long-answer set

Ultimate and Lifetime users can create one saved set of 4 extended-response questions for this topic and mark answers with examiner-style feedback.

AI MCQ generation is available to paying students: 20 questions per session,2 sessions per month. Long-answer AI generation requires Ultimate or Lifetime access.

Free starter set

Further Pure 2: Matrix Algebra: Edexcel Further Maths Optional Long-Answer Questions

Examiner-style long-answer practice with automatic marking, improvement advice and ProofCoach tracking.

4 questions32 marks64 min

standard / hard / synoptic

8 marksfindstandardEdexcel

FP14-1 Find the required result for Further Pure 2: Matrix Algebra. Given For A = [[4,1],[2,3]], find eigenvalues, eigenvectors and

A^{5}

using diagonalisation. Use solve the characteristic equation and form

PDP^{-1}

. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

8 marksshow thathardEdexcel

FP14-2 Show that the eigenvalues are 5 and 2 for Further Pure 2: Matrix Algebra. Start from For A = [[4,1],[2,3]], find eigenvalues, eigenvectors and

A^{5}

using diagonalisation. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

8 marksdeterminehardEdexcel

FP14-3 Determine the requested value in this structured Further Pure 2: Matrix Algebra problem: use

PDP^{-1}

to write an exact expression for

A^{5}

. Use the same data: For A = [[4,1],[2,3]], find eigenvalues, eigenvectors and

A^{5}

using diagonalisation. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

8 markshencesynopticEdexcel

FP14-4 Hence use the result the eigenvalues are 5 and 2 to complete the extension for Further Pure 2: Matrix Algebra: use

PDP^{-1}

to write an exact expression for

A^{5}

. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

Subject MCQ Bank

20 stored MCQs for this topic

Paying students get 20 stored MCQs per generation session and 2sessions each month. Your set is saved here so you can reset and retake it without using another allowance. If the bank is running low, replenishment happens in the background.

The 20-question stored MCQ bank is premium-only. Free users can study the starter unit and standard quiz, but bank practice unlocks after purchasing the subject.

Loading practice tools...

← Previous

13. Further Pure 2: Recurrence Relations

15. Further Pure 2: Integration Techniques

Key learning objectives

Understand the key principles behind Further Pure 2: Matrix Algebra.
Apply these ideas to exam-style questions.
Recall the essential definitions and key terms.