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Date May 2018 Marks available 3 Reference code 18M.1.AHL.TZ0.F_2
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Show that Question number F_2 Adapted from N/A

Question

Let A2 = 2A + I where A is a 2 × 2 matrix.

Show that A4 = 12A + 5I.

[3]
a.

Let B [ 4 2 1 3 ] .

Given that B2B – 4I [ k 0 0 k ] , find the value of k .

[3]
b.

Markscheme

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

METHOD 1
A4 = 4A2 + 4AI + I2 or equivalent       M1A1
= 4(2A + I) + 4A + I       A1
= 8A + 4I + 4A + I
= 12A + 5I      AG

[3 marks]

METHOD 2
A3 = A(2A + I) = 2A2 + AI = 2(2A + I) + A(= 5A + 2I)       M1A1
A4 = A(5+ 2I)       A1
= 5A2 + 2A = 5(2+ I) + 2A
= 12A + 5I       AG

[3 marks]

a.

B2 =  [ 18 2 1 11 ]       (A1)

[ 18 2 1 11 ] [ 4 2 1 3 ] [ 4 0 0 4 ] = [ 10 0 0 10 ]       (A1)

k = 10      A1

[3 marks]

b.

Examiners report

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

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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