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Date May Example question Marks available 2 Reference code EXM.1.AHL.TZ0.30
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Find Question number 30 Adapted from N/A

Question

Matrices A, B and C are defined as

A = ( 1 5 1 3 1 3 9 3 7 ) B = ( 1 2 1 3 1 0 0 3 1 ) C =  ( 8 0 4 ) .

Given that AB = ( a 0 0 0 a 0 0 0 a ) , find a .

[1]
a.

Hence, or otherwise, find A–1.

[2]
b.

Find the matrix X, such that AX = C.

[2]
c.

Markscheme

a = 16                    A1

[1 mark]

a.

A–1 1 16 ( 1 2 1 3 1 0 0 3 1 )                   (M1)A1

[2 marks]

b.

AX = C ⇒ X = A–1C                 (M1)

= 1 16 ( 1 2 1 3 1 0 0 3 1 ) ( 8 0 4 )

= 1 16 ( 12 24 4 ) ( = ( 0.75 1.5 0.25 ) )         A1

[2 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

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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