plumiFurther matrix algebra: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on FP3.6 Further matrix algebra, 2019–2025, with its mark scheme and examiner’s report.
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All 18 questions on Further matrix algebra, as a list
- June 2025, Further Pure 3 (FP3), Q3 (10 marks): M 1 1 4 3 1 a b a b where a and b are constants Given that i j k + + 2 is an eigenvector of M, (a) determine the corresponding eigenvalue. (b) Hen
- June 2025, Further Pure 3 (FP3), Q6 (7 marks): A 1 2 5 3 2 6 1 4 k where k is a constant (a) Determine the value of k for which A is singular. Given that A is non‑singular, (b) determine A –1,
- January 2025, Further Pure 3 (FP3), Q4 (14 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. 4 0 2 0 4 20 2 3 a a M
- June 2024, Further Pure 3 (FP3), Q2 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. M 2 0 3 0 4 3 0 4 0 Given tha
- January 2024, Further Pure 3 (FP3), Q2 (8 marks): T U 2 3 7 3 2 6 4 6 1 4 15 9 8 5 a b c a where a, b and c are constants. Given that TU = I (a) determine the value of a, the value of
- January 2024, Further Pure 3 (FP3), Q4 (8 marks): M 0 1 3 1 4 1 3 1 0 Given that 1 2 1 is an eigenvector of M (a) determine its corresponding eigenvalue. Given that –3 is an eigenvalue of
- June 2023, Further Pure 3 (FP3), Q2 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. M 2 0 0 0 1 4 3
- June 2023, Further Pure 3 (FP3), Q5 (7 marks): M 1 2 1 3 4 2 6 8 k k where is a constant Given that M has a repeated eigenvalue, determine (i) the possible values of k, (ii) all corresponding e
- January 2023, Further Pure 3 (FP3), Q5 (12 marks): where a is a positive constant (a) Determine the exact value of a for which the matrix A is singular. Given that 2 is an eigenvalue of A (b) determine (i) the v
- June 2022, Further Pure 3 (FP3), Q3 (8 marks): M = − − 2 5 0 5 1 3 0 3 6 Given that i + j + k is an eigenvector of M, (a) determine the corresponding eigenvalue. Given that 8 is an eigenvalue
- June 2022, Further Pure 3 (FP3), Q6 (8 marks): A = x x 1 3 2 4 4 2 1 − − − (a) Show that A is non‑singular for all real values of x. (b) Determine, in terms of x, A–1
- January 2022, Further Pure 3 (FP3), Q4 (9 marks): M = 6 5 0 2 0 7 k k where k is a constant. Given that 3 is an eigenvalue of M, (a) determine the possible values of k. Given that k < 0 (b) dete
- October 2021, Further Pure 3 (FP3), Q4 (11 marks): The matrix M is given by 2 0 1 3 2 2 1 − − k k (a) Show that det M = 5k − 10 Given that k ≠ 2 (b) find M−1 in terms of k. The points O (0, 0, 0)
- June 2021, Further Pure 3 (FP3), Q3 (9 marks): M = 3 1 1 1 2 1 2 p p − where p is a real constant (a) Find the exact values of p for which M has no inverse. Given that M does have an inverse,
- January 2021, Further Pure 3 (FP3), Q3 (6 marks): A = 2 2 2 2 1 2 2 k k where k is a constant (a) Determine the values of k for which A is singular. Given that A is non-singular, (b) find A−1 ,
- January 2021, Further Pure 3 (FP3), Q5 (9 marks): M = 6 2 1 2 6 1 1 1 5 − − − − − − Given that 8 is an eigenvalue of M (a) determine an eigenvector corresponding to the eigenvalue 8 (b) Determin
- October 2020, Further Pure 3 (FP3), Q3 (9 marks): M = − − − 3 4 1 2 1 5 5 k k where k is a constant Given that 3 is an eigenvalue of M, (a) find the value of k. (b) Hence find the other two eige
- October 2020, Further Pure 3 (FP3), Q6 (8 marks): A = 1 1 1 1 1 1 1 2 1 − ≠ a a (a) Find A−1 in terms of a. B = 1 1 1 1 1 1 1 2 4 − The straight line l1 is mapped onto the straig
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