User interface language: English | Español

Date May Example question Marks available 2 Reference code EXM.1.AHL.TZ0.26
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Calculate Question number 26 Adapted from N/A

Question

Consider the matrices

A = ( 3 2 5 4 ) , B ( 1 3 2 2 ) .

Find BA.

[2]
a.

Calculate det (BA).

[2]
b.

 Find A(A–1B + 2A–1)A.

[3]
c.

Markscheme

BA ( ( 1 3 2 2 ) ( 3 2 5 4 ) ) = ( 18 14 4 4 )              A2 

Note: Award A1 for one error, A0 for two or more errors.

[2 marks]

a.

det(BA) = (72 – 56) = 16            (M1)A1 

[2 marks]

b.

EITHER            

A(A–1B + 2A–1)A = BA + 2A            (M1)A1

= ( 24 18 6 4 )         A1

OR

A–1  = 1 2 ( 4 2 5 3 )             (A1)

an attempt to evaluate            (M1)

A–1B + 2A–1 = 1 2 ( 0 16 1 21 ) ( 4 2 5 3 )

A(A–1B + 2A–1)A =  ( 3 2 5 4 ) ( 4 6 4.5 7.5 ) ( 3 2 5 4 )

= ( 3 3 2 0 ) ( 3 2 5 4 ) = ( 24 18 6 4 )               A1 

[3 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
Show 139 related questions
Topic 1—Number and algebra

View options