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A-LevelFurther MathematicsMatrices9231/12 · Oct/Nov 2017 · Q710 Marks

The linear transformation T : R⁴ → R⁴ is represented by the matrix A, where A = [[1, -1, -2, 3], [5, -3, -4, 25], [6, -4, -6, 28], [7, -5, -8, 31]].

  1. (i)Find the rank of A and a basis for the null space of T.[7]
  2. (ii)Find the matrix product A [[1], [-1], [-1], [1]] and hence find the general solution of the equation Ax = [[3], [21], [24], [27]].[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

  1. [2] M1A1
  2. [1] A1
  3. [1] B1
  4. [1] M1
  5. [2] A1A1 OE
  6. [1] B1
  7. [2] M1A1FT OE

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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 2017 Paper 1 Variant 2, question 7.

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