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AS & A Level · AS/A Level

Further Mathematics

Proof and linear algebra

Name: ____________________Date: October 10, 2026
  1. 1.

    For A = [[1, 2], [3, 4]], calculate det(A) and A^-1.

    [3 marks] · no calculator
  2. 2.

    Prove by mathematical induction that 1 + 3 + ... + (2n - 1) = n^2 for every positive integer n.

    [4 marks] · no calculator
  3. 3.

    Let A = [[2, 1], [1, 2]] and P = [[1, 1], [1, -1]]. Show A = P diag(3, 1) P^-1 and deduce a formula for A^n for positive integer n.

    [4 marks] · no calculator

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