O-LevelAdditional MathematicsEquations, inequalities and graphs4037/12 · Oct/Nov 2016 · Q67 Marks

Matrices X, Y and Z are such that X = ((2, 3), (4, -1), (6, 5)), Y = (1 -1 0) and Z = ((0, -1), (5, 3)). Write down all the matrix products which are possible using any two of these matrices. Do not evaluate these products.

(a)Matrices X, Y and Z are such that X = ((2, 3), (4, -1), (6, 5)), Y = (1 -1 0) and Z = ((0, -1), (5, 3)). Write down all the matrix products which are possible using any two of these matrices. Do not evaluate these products.[2]
(b)(i)Matrices A, B and C are such that A = ((2, -1), (4, 7)), B = ((-4, 2), (10, 4)) and AC = B. Find A⁻¹.[2]
(b)(ii)Hence find C.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.

[2] (a) YX, XZ B2 for both with no extras B1 for 1 correct with or without extras B1 for both correct with extras B0 for anything else
[2] (b)(i) 1/18 ((7, 1), (-4, 2)) B1 for 1/18 B1 for ((7, 1), (-4, 2))
[1] (b)(ii) C = A⁻¹B M1 for pre-multiplication
[2] (b)(ii) C = ((-1, 1), (2, 0)) A1 for any correct pair of elements, but must be from correct matrices

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Topic: Equations, inequalities and graphs, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2016 Paper 1 Variant 2, question 6.

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