Cambridge Additional Mathematics

(singke) #1
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

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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

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