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A-LevelFurther MathematicsMatrices9231/12 · May/June 2015 · Q26 Marks

Find the value of the constant k for which the system of equations 2x - 3y + 4z = 1, 3x - y = 2, x + 2y + kz = 1, does not have a unique solution. For this value of k, solve the system of equations.

Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

  1. [M1A1] |2 -3 4 / 3 -1 0 / 1 2 k| = 0 ⇒ 7k - 28 = 0 ⇒ k = -4
  2. [M1] Add 1st and 3rd ⇒ 3x − y = 2 ( Same as 2nd) (OE)
  3. [M1] Set x = t (for example) (OE)
  4. [A1A1] ⇒ y=3t-2, z=-7/4 t - 5/4 (OE) - many forms

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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 2015 Paper 1 Variant 2, question 2.

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