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Date May Example question Marks available 1 Reference code EXM.1.AHL.TZ0.16
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Write down Question number 16 Adapted from N/A

Question

Find a relationship between a and b  if the matrices  M = ( 1 a 2 3 ) and  N = ( 1 b 2 3 )  commute under matrix multiplication.

[4]
a.

Find the value of a  if the determinant of matrix  M is −1.

 

[2]
b.i.

Write down  M 1 for this value of a .

[1]
b.ii.

Markscheme

( 1 a 2 3 ) ( 1 b 2 3 ) = ( 1 + 2 a b + 3 a 8 2 b + 9 )

( 1 b 2 3 ) ( 1 a 2 3 ) = ( 1 + 2 b a + 3 b 8 2 a + 9 )         M1A1

So require  a = b        M1A1

[4 marks]

a.

| 1 a 2 3 | = 3 2 a = 1 a = 2        M1A1

[2 marks]

b.i.

( 1 2 2 3 ) 1 = ( 3 2 2 1 )        A1

[1 mark]

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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