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A-LevelFurther MathematicsMatrices9231/12 · May/June 2017 · Q46 Marks

Find the value of k for which the set of linear equations x + 3y + kz = 4, 4x-2y - 10z = −5, x + y + 2z = 1, has no unique solution.

  1. (i)Find the value of k for which the set of linear equations x + 3y + kz = 4, 4x-2y - 10z = −5, x + y + 2z = 1, has no unique solution.[3]
  2. (ii)For this value of k, find the set of possible solutions, giving your answer in the form ( x y z )ᵀ = a + tb, where a and b are vectors and t is a scalar.[3]

Mark scheme

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

  1. [M1]
  2. [A1]
  3. [A1]
  4. [M1A1]
  5. [A1 FT] Alternative: Find REF for augmented matrix and form equations (M1) Correctly (A1)

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About this question

Topic
Matrices, A-Level Further Mathematics (syllabus 9231). Structured question, 6 marks.
Source
A-Level Further Mathematics, May/June 2017 Paper 1 Variant 2, question 4.

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