Cambridge Additional Mathematics

318 Matrices (Chapter 12)

Example 6 Self Tutor

For A=

¡

135

¢

, B=

μ

135

213

¶

, and C=

0

@

10

23

14

1

A, find: a AC b BC

a Ais 1 £ 3 andCis 3 £ 2 ) ACis 1 £ 2

AC=

¡

135

¢

0

@

10

23

14

1

A

=

¡

1 £1+3£2+5£ 11 £0+3£3+5£ 4

¢

=

¡

12 29

¢

b Bis 2 £ 3 andCis 3 £ 2 ) BCis 2 £ 2

BC=

μ

135

213

¶

0

@

10

23

14

1

A

=

μ

1 £1+3£2+5£ 11 £0+3£3+5£ 4

2 £1+1£2+3£ 12 £0+1£3+3£ 4

¶

=

μ

12 29

715

¶

EXERCISE 12C.2

1 Explain whyABcannot be found for A=

¡

421

¢

and B=

μ

121

010

¶

.

2 SupposeAis 2 £n andBis m£ 3.

a When can we findAB? b IfABcan be found, what is its order?

c Explain whyBAcannot be found.

3 For A=

μ

21

34

¶

and B=

¡

56

¢

, find: a AB b BA

4 For A=

¡

203

¢

and B=

0

@

1

4

2

1

A, find: a AB b BA

5 Find: a

¡

121

¢

0

@

231

010

102

1

A b

0

@

10 ¡ 1

¡11 0

0 ¡ 11

1

A

0

@

2

3

4

1

A

6 Answer theOpening Problemon page 306.

X

X

To get the element in the nd

row and st column of ,

multiply the nd row of

by the st column of.

2

1

2

1

BC

B

C

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_12\318CamAdd_12.cdr Tuesday, 7 January 2014 5:57:06 PM BRIAN