plumiEigenvalues, eigenvectors and diagonalisation: OCR MEI A‑Level Further Maths questions
OCR MEI A-Level Further Maths past-paper questions on 3.7 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 9 questions on Eigenvalues, eigenvectors and diagonalisation, as a list
- June 2025, Extra Pure, Q5 (14 marks): In this question you must show detailed reasoning. J N a b 0 K O 2 2 The matrix A is given by b a 0 OO where a and b are constants with a b = and a 1 1 . KK - +
- June 2024, Extra Pure, Q4 (15 marks): K O 4 The matrix P is given by P = - 6 12 12 OO. KK 2 4 8 - L P 3 2 (a) Show that the characteristic equation of P is 21 126 216 0 . [3] - m + m - m + = You are
- June 2023, Extra Pure, Q5 (15 marks): J N a 0 KK OO where a is a constant and a 5 The matrix P is given by P ! . 3 = 2 3 L P 1 r radians, (a) Given that the acute angle between the directions of the
- June 2022, Extra Pure, Q2 (12 marks): K O 2 The matrix A is given by A 1 2 4 . = - KK OO 3 6 2 L P (a) In this question you must show detailed reasoning. 3 2 Show that the characteristic equation of
- November 2021, Extra Pure, Q3 (14 marks): K O 3 The matrix A is given by A 0 2 2 OO. = KK 1 3 4 L P (a) Determine the characteristic equation of A. [3] (b) Hence verify that the eigenvalues of A are 1,
- November 2020, Extra Pure, Q1 (5 marks): J N 0 2 KK OO. 1 The matrix A is given by A = 3 1 - L P Find • the eigenvalues of A, • an eigenvector associated with each eigenvalue. [5]
- November 2020, Extra Pure, Q5 (8 marks): In this question you must show detailed reasoning. J N 1 2 2 - - K O J N 1 3 3 3 K O K O 2 1 2 The matrix A is given by and the vector e is given by OO. You are
- June 2019, Extra Pure, Q1 (5 marks): J N 0 6 . 0 8 . KK OO. 1 The matrix A is 0 8 . 0 6 . - L P (a) Given that A represents a reflection, write down the eigenvalues of A. [1] (b) Hence find the eig
- June 2019, Extra Pure, Q3 (8 marks): K O 3 The matrix A is 0 1 25 OO. - - KK 3 5 1 - - L P Use the Cayley-Hamilton theorem to find A−1. [8]
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