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Date May Example question Marks available 2 Reference code EXM.2.AHL.TZ0.6
Level Additional Higher Level Paper Paper 2 Time zone Time zone 0
Command term Write down Question number 6 Adapted from N/A

Question

Matrices A, B and C are defined by

( 5 1 7 2 )    B =  ( 2 4 3 15 )    C = ( 9 7 8 2 ) .

Let X be an unknown 2 × 2 matrix satisfying the equation

AX + B = C.

This equation may be solved for X by rewriting it in the form

X = A−1 D.

where D is a 2 × 2 matrix.

Write down A−1.

[2]
a.

Find D.

[3]
b.

Find X.

[2]
c.

Markscheme

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

A−1 ( 2 3 1 3 7 3 5 3 ) or  1 3 ( 2 1 7 5 )  or  ( 0.667 0.333 2.33 1.67 )          (A1)(A1)(N2)

[2 marks]

a.

AX = C − B (may be implied)        (A1)

X = A−1 (CB)        (A1)

D = C  B    

= ( 7 11 11 13 )         (A1)  (N3)

[3 marks]

b.

X = ( 1 3 2 4 )        (A2)  (N2)

[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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