O-LevelAdditional MathematicsSimultaneous equations4037/11 · May/June 2011 · Q88 Marks

The matrices A, B and C are given by A = (2 1 / 1 3 / 2 5), B = (2 1 3 4 / 1 5 6 7) and C = (9 10). Write down, but do not evaluate, matrix products which may be calculated from the matrices A, B and C.

(a)The matrices A, B and C are given by A = (2 1 / 1 3 / 2 5), B = (2 1 3 4 / 1 5 6 7) and C = (9 10). Write down, but do not evaluate, matrix products which may be calculated from the matrices A, B and C.[2]
(b)Given that X = (2 4 / 3 5) and Y = (2x 3y / x 4y), find the value of x and of y such that X⁻¹Y = (-12x+3y 6 / -7x+3y 6).[6]

Mark scheme

Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.

[2] B2,1,0 for products AB and AC. (-1 for each incorrect or extra product.)
[1] M1 for pre-multiplying by X to get Y = X * (-12x+3y 6 / -7x+3y 6).
[1] M1 for performing matrix multiplication: (2 4 / 3 5) * (-12x+3y 6 / -7x+3y 6).
[2] M1A1 for correct product matrix: (-52x+18y 36 / -71x+24y 48).
[1] M1 for equating like elements from Y and the product matrix to form simultaneous equations.
[1] A1A1 for x=4 and y=12.

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