3rd Edition Aslam Kassimali
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,Chapter 2
17
10 1
1 4 3
2.1
C A
B
4 4 4 ; D A
B 10
14 4
3
4 0
1
4 12
1
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,
17
4
12
7
9 5
20
7
2.2
C 2 A
B
12
3 0 19 ; D A
3B
20
19 21
15
11
2 2 9
2
8
27 22
2
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,
5
15 35
5 30
2 6
14 2
12
2.3 C AB 3
7 1
6
8
24 56
8 48
4
12
28 4
24
5
2
D BA 3
7 1
6
15
14
8
24
61
8
4
3
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,
2
10
1
10
2
6 6
1
84
74
2.4 C AB
3
8
12 8
2 10
22
70
5 9
2
10
28 60 116 68
6
1
1
10
2
6 3
52 0
28
D BA
2 10
3
8
12 8 28 60
116
68
5 9
32
122
118
102
4
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,
5 7
2
2
8 1
48
29 28
2.5 C AB 7 9 0
8 3 5
588
29 52
2 0 8
1 5 6
4 56 46
2
8 1
5 7
2
48
58 4
D BA
8 3 5 7 9 0
29
29 56
1 5 6
2 0 8
28 52 46
5
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,
3 4 2
8 1 6
2
54
5 36 26
2.6 C AB 2 3
8 6
2 5 8 10
4 35 20
3 0 6
3 0
1 0
6
3
24 6
6
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,
12
7 6 0
14
5 11
268
1877
46 153
2.8 AB 2 9 15
13
3 18
9 10
4
90 219 297
306
5 8
268
90
187 219
AB
T
(1)
46 297
153
306
12 2 10
268
90
7 9
4
14
3
5
187 219
BT A T 18 (2)
6 15
5
46 297
11
9
0
13 8
153
306
From Eqs. (1) and (2), we can see that AB
BT AT .
T
7
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, −9 0
13 −7 10 6 0
20 15 −1 −4
2.9 [ A][ B][C ] = 8 −1 2 −8 −2
−3 6 16 9
16 12 2 8
−11 −5
−135 9 36
315 −7 10 6 0
307 128
= −1 2 −8 −2
102 −56 −59
16 12 2 8
−195 −69 −1
1512 −900 −810 270
−464 5300 −310 410
=
−1602 200 942 −360
1418 −2100 −620 130
1512 −464 −1602 1418
−900 5300 200 −2100
([ A][ B][C ]) =
T
(1)
−810 −310 942 −620
270 410 −360 130
−7 −1 16
10 15 6
2 12 −9 13 8 −11
[ C ] [ B ] [ A] = 16
T T T
−1
6 −8 2 0 20 −3 −5
−4 9
0 −2 8
−168 86
100 200 −9 13 8 −11
=
90 −74 0 20 −3 −5
−30 40
1512 −464 −1602 1418
−900 5300 200 −2100
= (2)
−810 −310 942 −620
270 410 −360 130
From Eqs. (1) and (2), we can see that
([ A][ B ][C ]) = [C ] [ B ] [ A]
T T T T
88
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© 2022 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.