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Date May Example question Marks available 2 Reference code EXM.1.AHL.TZ0.4
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Find Question number 4 Adapted from N/A

Question

Consider the matrix = ( 5 2 7 1 ) .

B, C and X are also 2 × 2 matrices.

Write down the inverse, A–1.

[2]
a.

Given that XA + B = C, express X in terms of A–1, B and C.

[2]
b.i.

Given that B = ( 6 7 5 2 ) , and C = ( 5 0 8 7 ) , find X.

[2]
b.ii.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

det A = 5(1) − 7(−2) = 19

A–1  = 1 19 ( 1 2 7 5 ) = ( 1 19 2 19 7 19 5 19 )        (A2)

Note: Award (A1) for  ( 1 2 7 5 ) (A1) for dividing by 19.

OR

A–1  = ( 0.0526 0.105 0.368 0.263 )                       (G2)

[2 marks]

a.

XA + B = C XA = CΒ        (M1)

X = (C Β)Α–1   (A1)

OR

X = (CB)A–1       (A2)

[2 marks]

b.i.

(C Β)Α–1 = ( 11 7 13 9 ) ( 1 19 2 19 7 19 5 19 )        (A1)

X = ( 38 19 57 19 76 19 19 19 ) = ( 2 3 4 1 )    (A1)

OR

X = ( 2 3 4 1 )        (G2)

Note: If premultiplication by A–1 is used, award (M1)(M0) in part (i) but award (A2) for  ( 37 19 11 19 12 19 94 19 )  in part (ii).

[2 marks]

b.ii.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.

Syllabus sections

Topic 1—Number and algebra » AHL 1.14—Introduction to matrices
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Topic 1—Number and algebra

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