plumiEigenvalues, eigenvectors and diagonalisation: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 8.1 Eigenvalues, eigenvectors and diagonalisation, 2018–2025, 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 13 questions on Eigenvalues, eigenvectors and diagonalisation, as a list
- June 2025, Further Pure 2, Q2 (8 marks): A 1 2 2 4 (a) Determine the eigenvalues of matrix A (3) (b) Hence determine an orthogonal matrix P and a diagonal matrix D such that D = P TAP (5)
- June 2025, AS Further Pure 2, Q4 (7 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. A = 6 1 2 3 Determine a
- June 2024, Further Pure 2, Q4 (12 marks): A = 4 2 0 2 2 0 2 2 p where p is a constant Given that 2 1 2 is an eigenvector of A, (a) determine the eigenvalue corresponding to this eigenv
- June 2023, Further Pure 2, Q1 (6 marks): A 1 3 8 a where a is a constant. (a) Determine, in expanded form in terms of a, the characteristic equation for A. (2) (b) Hence use the Cayley-Hamilton
- June 2023, AS Further Pure 2, Q2 (8 marks): A linear transformation T : 2 → 2 is represented by the matrix M 5 1 3 k where k is a constant. Given that matrix M has a repeated eigenvalue, (a) de
- June 2022, Further Pure 2, Q2 (8 marks): Matrix M is given by M = 1 3 0 0 1 1 b a a where a and b are integers, such that a < b Given that the characteristic equation for M is λ3 – 7λ2 + 13λ +
- June 2022, AS Further Pure 2, Q2 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. M 4 3 2 1 Find a matrix P and a
- November 2021, Further Pure 2, Q8 (17 marks): A = 5 2 5 0 3 6 6 4 − − − p where p is a constant Given that 2 1 2 − is an eigenvector for A (a) (i) determine the eigenvalue co
- November 2020, Further Pure 2, Q3 (10 marks): M = 1 2 2 4 1 1 2 3 k − − where k is a constant. (a) Show that, in terms of k, a characteristic equation for M is given by λ3 – (2k + 13)λ + 5(k
- November 2020, AS Further Pure 2, Q3 (10 marks): (i) A = 1 2 1 4 − (a) Show that the characteristic equation for A is λ2 – 5λ + 6 = 0 (2) (b) Use the Cayley‑Hamilton theorem to find integers p and q
- June 2019, Further Pure 2, Q2 (11 marks): The matrix A is given by A = − − − − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ 6 2 2 1 2 1 (a) Show that 2 is a repeated eigenvalue of A and find the other eigenvalue. (5) (b) Henc
- June 2019, AS Further Pure 2, Q1 (5 marks): Given that A = ⎛ ⎝⎜ ⎞ ⎠⎟ 3 2 2 2 (a) find the characteristic equation for the matrix A, simplifying your answer. (2) (b) Hence find an expression for the matrix
- June 2018, AS Further Pure 2, Q4 (7 marks): A = 1 1 2 4 − Find a matrix P and a diagonal matrix D such that D = P–1AP (7)
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