plumiEigenvalues, eigenvectors and diagonalisation: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on C.7 Eigenvalues, eigenvectors and diagonalisation, 2019–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 5 questions on Eigenvalues, eigenvectors and diagonalisation, as a list
- June 2025, Paper 1, Q12 (13 marks): (a) Find the eigenvalues and corresponding eigenvectors of the matrix = 19 3 1 3 11 20 M [5 marks] 12 (b) State, with a reason, the Cartesian equati
- June 2023, Paper 1, Q6 (11 marks): The matrix M is given by M = 1 10 a a −6 0 10 0 9 14 −13 2 664 3 775 where a is a real number. The vectors v1, v2, and v3 are eigenvectors of M The correspondin
- June 2022, Paper 1, Q4 (1 mark): The vector v is an eigenvector of the matrix N with corresponding eigenvalue 4 The vector v is also an eigenvector of the matrix M with corresponding eigenvalue
- June 2022, Paper 2, Q11 (9 marks): (a) Find the eigenvalues and corresponding eigenvectors of the matrix M = 5 2 −3 2 −3 2 13 2 2 64 3 75 [5 marks] 11 (b) (i) Describe how the directions of the i
- June 2019, Paper 2, Q9 (13 marks): (a) Find the eigenvalues and corresponding eigenvectors of the matrix M = 1 5 2 5 −3 5 13 10 2 6664 3 7775 [5 marks] 9 (b) Find matrices U and D such that D is
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