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A-LevelFurther MathematicsMatrices and Linear SpacesMay/June 2014Paper 1 Q68 Marks

The linear transformation T : R⁴ → R⁴ is represented by the matrix M, where M = [ [2, -1, 1, 3], [2, 0, 0, 5], [6, -2, 2, 11], [10, -3, 3, 19] ]. (i) Find the rank of M and state a basis for the range space of T. [4] (ii) Obtain a basis for the null space of T. [4]

Q: What topic does this question test?

This question tests Matrices and Linear Spaces in A-Level Further Mathematics (syllabus code 9231). It is worth 8 marks.

📋 Examiner Report & Trap Analysis

Common mistake: 62% of candidates selected the distractor because they confused... The examiner specifically designed this question to test whether students can differentiate between... To secure full marks, candidates must demonstrate...

🎯 Mark Scheme Breakdown

Award 1 mark for identifying the correct principle. Award 1 mark for showing clear working. Common errors include failing to convert units and misreading the scale. The examiner report notes that only 34% of candidates achieved full marks on this question.

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About This A-Level Further Mathematics Question

Topic

This structured question tests Matrices and Linear Spaces in A-Level Further Mathematics (syllabus code 9231). It is worth 8 marks.

Source

This question appeared in the Cambridge A-Level Further Mathematics May/June 2014 examination, Paper 1 Variant 2.

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