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O-LevelAdditional MathematicsSimultaneous equations4037/12 · Oct/Nov 2014 · Q76 Marks

Matrices A and B are such that A = ( (3a, 2b), (-a, b) ) and B = ( (-a, b), (2a, 2b) ) where a and b are non-zero constants.

  1. (i)Find A⁻¹.[2]
  2. (ii)Using your answer to part (i), find the matrix X such that XA = B.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.

  1. [2] B1 for 1/(5ab), B1 for ( (b, -2b), (a, 3a) )
  2. [1] M1 for post-multiplication by inverse matrix X = BA⁻¹
  3. [1] DM1 for correct attempt at matrix multiplication, needs at least one term correct for their BA⁻¹ (allow unsimplified)
  4. [2] A1 A1 for each correct pair of elements, must be simplified ( (0, 1), (4, 2), (5, 5) )

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About this question

Topic
Simultaneous equations, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2014 Paper 1 Variant 2, question 7.

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