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A-LevelFurther MathematicsMatrices9231/12 · Oct/Nov 2019 · Q810 Marks

The matrix M is defined by M = [[2,m,1],[0,m,7],[0,0,1]] where m ≠ 0, 1, 2.

  1. (i)Find a matrix P and a diagonal matrix D such that M = PDP-1.[7]
  2. (ii)Find M7P.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

  1. [B1] Eigenvalues of (upper diagonal matrix) A are 2,m and 1. (Or from characteristic equation: (λ-2)(λ-m)(λ-1) = 0)
  2. [M1 A1] Uses vector product (or equations) to find corresponding eigenvectors.
  3. [A1]
  4. [A1]
  5. [M1 A1 FT] Or correctly matched permutations of columns. No follow through on two or more zero eigenvectors.

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About this question

Topic
Matrices, A-Level Further Mathematics (syllabus 9231). Structured question, 10 marks.
Source
A-Level Further Mathematics, Oct/Nov 2019 Paper 1 Variant 2, question 8.

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