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