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1; : : : ; 52664
10
!23
3775
2664
0123
3775
2664
2!2!8
0
3775
2664
2!1103
3775
2664
3!1!6
9
3775
2664
1001
3775
2664
!2002
3775
2664
3!1
1!1
3775
2664
5!3
3!4
3775
2664
2!1
10
3775
266664
20
!4!6
0
377775
266664
402
!44
377775
266664
!2!4
01
!7
377775
266664
848
!315
377775
266664
!84001
377775
266664
!3260
!7
377775
266664
30
!906
377775
266664
02
!40
!1
377775
266664
6!2
!140
13
377775
266664
!630
!10
377775
1 D
24
4!3
7
35
2 D
24
19
!2
35
3 D
24
7116
35
H D f 1; 2; 3g 4 1 C 5 2 !3 3 D H
1 D
2664
34
!2!5
3775 2 D
2664
4324
3775 3 D
2664
25
!6!14
3775
2 1 ! 2 ! 3 DH D f 1; 2; 3g
H D f 1; : : : ; pg f 1; : : : ; pgH
n % nRn
HH
SV S V
AA
B AB A
R4 D f 1; : : : ; 4g f 1; : : : ; 4gR4
B D f 1; : : : ; ng Rn
B Rn
1 D
24
101
35
2 D
24
011
35
3 D
24
010
35 H
R3
H
1; 2; 324
stt
35 D s
24
101
35 C .t ! s/
24
011
35 C s
24
010
35
s t f 1; 2; 3g H
f t; 2t; t tgV
V
R L Cb D R=.2L/ R
L C b 1=p
LC
v.t/ tv
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v.t/ D e"bt .c1 C c2t/H
Voltagesource
L
R
C
Rn
n
S D f 1; : : : ; kg k Rn k < nS
Rn
S D f 1; : : : ; kg k Rn k > nS
Rn
V WT W V ! W
f 1; : : : ; pg V
f 1; : : : ; pg VfT . 1/; : : : ; T . p/g
Wf 1; : : : ; pg
fT . 1/; : : : ; T . p/g
TT . / D T . / D
fT . 1/; : : : ; T . p/gf 1; : : : ; pg
1.t/ D 1 C t 22.t/ D 1 !
t 2 f 1; 2g P3
1.t/ D 1 C t 2.t/ D 1 ! t
3.t/ D 2 t
1 2 3
f 1; 2; 3gV
f 1; 2; 3; 4gf 1; 2; 3; 4g V f 1; 3g
f 1; 2; 3; 4gH D f 1; 2; 3g K D f 1; 2; 3g
1 D
2664
120
!1
3775; 2 D
2664
02
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3775; 3 D
2664
341
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3775;
1 D
2664
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3
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2664
232
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24
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f 1; 2g R31
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1 6 2 !4!3 2 !2 !8
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A
1 2 H f 1; 2g H f 1; 2g.c1; c2; 0/ H
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D c1 1 C # # # C cn n
B V
D d1 1 C # # # C dn n
d1; : : : ; dn
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1 $ j $ n
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264
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1
#
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35
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113
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.t/ D 1 C 3t ! 6t2
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BV
V B n BRn
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P3 R3
B Rn BRn
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1!3
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1; : : : ; n n % n
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S S V
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9
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2 % 2 AA
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B D f 1; : : : ; ng Rn
n % n A7! Œ !B
V B Df 1; : : : ; ng 7! Œ !B
Œ !B D Œ !B VD
Rn
Rn y1; : : : ; yn VŒ !B D
f 1; : : : ; pg V
fŒ 1 !B; : : : ; Œ p !Bg Rn
c1; : : : ; cp
c1 1 C # # # C cp p D VŒ c1 1 C # # # C cp p !B D Œ !B Rn
1; : : : ; p V
1; : : : ; p Œ !BŒ 1 !B; : : : ; Œ p !B
1 C 2t3 2 C t ! 3t2 !t C 2t2 ! t 3
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1 ! 3t C 5t2 !3 C 5t ! 7t2 !4 C 5t ! 6t2 1 ! t 2
5t C t 2 1 ! 8t ! 2t2 !3 C 4t C 2t2 2 ! 3t
1.t/ D 1 C t 22.t/ D t ! 3t2
3.t/ D 1 C t ! 3t2
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B D f 1; 2; 3g P2 P2
Œ !B D
24
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35
P3
3 C 7t; 5 C t ! 2t3; t ! 2t2; 1 C 16t ! 6t2 C 2t3
5 ! 3t C 4t2 C 2t3; 9 C t C 8t2 ! 6t3; 6 ! 2t C 5t2; t 3
H D f 1; 2g B D f 1; 2gH B
1 D
2664
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3775; 2 D
2664
14!81310
3775; D
2664
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1815
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1 D
2664
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3775; 2 D
2664
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2664
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2664
47
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3775
24
2:6!1:5
0
35
24
030
35
24
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35
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35
R3
PB D Œ 1 2 3 !PB
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24
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35
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35
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&
24
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35
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24
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35
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t
c1 C c2 D 6
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c2 C c3 D !1
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24
51
!2
35
V B nRn n
V
Rn
V B D f 1; : : : ; ng Vn
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p n c1; : : : ; cp
c1Œ 1 !B C # # # C cpŒ p !B D
264
0:::0
375 Rn
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264
0:::0
375
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f 1; : : : ; pg S p > nS
S pV p V D p S
V S p VV S 0 S V
V D p S 0 p S D S 0
A A
A AA A
AAA m % n A D k
Ak 1; : : : ; k
f 1; : : : ; kg A
A A DA A
A D
24
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35
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24
1 !2 2 3 !1 00 0 1 2 !2 00 0 0 0 0 0
35
x2 x4 x5 AA D 2 A
V
V D p S V Sp
S V T V S T
8<:
24
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8<ˆ:
2664
p C 2q!p
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3775 W p q R
9>>=>>;
8<ˆ:
2664
p ! 2q2p C 5r
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3775 W p q r R
9>>=>>;
8<ˆ:
2664
3a ! c!b ! 3c
!7a C 6b C 5c!3a C c
3775 W a b c R
9>>=>>;
f.a; b; c/ W a ! 3b C c D 0; b ! 2c D 0; 2b ! c D 0g
f.a; b; c; d/ W a ! 3b C c D 0g
R3
H R2"1
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# "!210
# "!315
#
24
102
35
24
311
35
24
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1
35
24
522
35
24
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0
35
24
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0
35
24
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35
24
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35
A A
A D
2664
1 !6 9 0 !20 1 2 !4 50 0 0 5 10 0 0 0 0
3775
A D
2664
1 2 !4 3 !2 6 00 0 0 1 0 !3 70 0 0 0 1 4 !20 0 0 0 0 0 1
3775
A D
24
1 2 3 0 00 0 1 0 10 0 0 1 0
35 A D
"3 2
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#
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24
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35 A D
24
1 1 !10 2 00 0 0
35
V
R3 R3
P4
V D n S VS V
f 1; : : : ; pgV T p V
T
R2 R3
A DA
V D n S V S V
R3 R3
2t !2 C 4t2
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1 ! t 2 ! 4t C t 2
6 ! 18t C 9t2 ! t 3
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B P3
.t/ D !1 C 8t2 C 8t3
B
B P2
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B
S n VS n S
V
H n nV H D V
P
2
C.R/
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f 1; : : : ; pg VV $ p
f 1; : : : ; pgV V " p
V D p p C 1V
f 1; : : : ; pg VV $ p
p V VV > p
p " 2 V D p p ! 1
VW T W V ! W
H V T .H/H T .H/ W
T .H/ $ H
H V TV W
T .H/ D H TV W V D W
f 1; : : : ; kg Rn Rn
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1; : : : ; n
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1 D
266664
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7
377775
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266664
9416
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377775
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266664
67
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377775
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B D f1; t; 2 t; : : : ; 6 tg C D f1; t;2t; : : : ; 6tg
2t D !1 C 2 2 t
3t D !3 t C 4 3 t
4t D 1 ! 8 2 t C 8 4 t
5t D 5 t ! 20 3 t C 16 5 t
6t D !1 C 18 2 t ! 48 4 t C 32 6 t
HB B H
B CC
H
C H
f gS V S 0
T S 0 T
40 % 50 AA
AT A
A
x
"5 75 x
#
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AA A A
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A D
2664
2 !1 1 !6 81 !2 !4 3 !2
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3775; B D
2664
1 !2 !4 3 !20 3 9 !12 120 0 0 0 00 0 0 0 0
3775
A A
A A
A
AT
A BA A
A A A
A D
24
1 !4 9 !7!1 2 !4 1
5 !6 10 7
35
B D
24
1 0 !1 50 !2 5 !60 0 0 0
35
A D
2664
1 3 4 !1 22 6 6 0 !33 9 3 6 !33 9 0 9 0
3775
B D
2664
1 3 4 !1 20 0 1 !1 10 0 0 0 !50 0 0 0 0
3775
A D
2664
2 6 !6 6 3 6!2 !3 6 !3 0 !6
4 9 !12 9 3 12!2 3 6 3 3 !6
3775
B D
2664
2 6 !6 6 3 60 3 0 3 3 00 0 0 0 3 00 0 0 0 0 0
3775
A D
266664
1 1 !2 0 1 !21 2 !3 0 !2 !31 !1 0 0 1 61 !2 2 1 !3 01 !2 1 0 2 !1
377775
B D
266664
1 1 !2 0 1 !20 1 !1 0 !3 !10 0 1 1 !13 !10 0 0 0 1 !10 0 0 0 0 1
377775
4 % 7 A A AAT
7 % 5 A A AAT
4 % 7 AA D R4 A D R3
6 % 8 AA A D R4
4 % 6 AA A D R3
8 % 7 AA
8 % 5 AA
5 % 4 AA
A 7 % 5 AA 5 % 7 A
A 5 % 4A A 4 % 5
A
A 3 % 7A
A 7 % 5A
A m % n
AAT
B A BA
A
A A
A A
B AB A
A
AA
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A
A B
m % n
m % n AA
A A A AT
AT AT Rm Rn
A C A D n A
A C AT D m A
A DRm AT D
A m % n Rm
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m % n AA D T
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24
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24
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35
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A
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266664
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6 !8 !5 4 4 9 3
377775
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A
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6 % 7A A
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5 % 7 ACR A A
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A A
f 1; 2g D
8<ˆ:
2664
21
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3775;
2664
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8!5
3775
9>>=>>;
B A f.1; !2; !4; 3; !2/.0; 3; 9; !12; 12/g A
AA A A
A BA
AT D A AT D A AT
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1 D"
1!3
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4
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9
#2 D
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7
#
R2 B D f 1; 2g C D f 1; 2gC BB C
PB C
PC B
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#
PB C D
"5 36 4
#
B C
PC B D . P
B C /!1 D 1
2
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#
PC B
PB PC B CRn
PBŒ !B D ; PCŒ !C D ; Œ !C D P !1C
Œ !C D P !1C D P !1
C PBŒ !B
Rn PC B P !1
C PB2 % 2
P !1C P !1
C PB
F D f 1; 2g G D f 1; 2g V PŒ 1 !G Œ 2 !G
P V
Œ !F D P Œ !G Œ !G D PŒ !F
B CC B
B D f 1; 2g C D f 1; 2gV 1 D 6 1 ! 2 2 2 D 9 1 ! 4 2
B CŒ !C D !3 1 C 2 2
B D f 1; 2g C D f 1; 2gV 1 D !2 1 C 4 2 2 D 3 1 ! 6 2
B CŒ !C D 2 1 C 3 2
U D f 1; 2g W D f 1; 2g VP Œ 1 !W Œ 2!W
P V
Œ !U D P Œ !W Œ !W D P Œ !U
A D f 1; 2; 3g D D f 1; 2; 3g VP D Œ Œ 1!A Œ 2!A Œ 3!A !
P V
Œ !A D P Œ !D Œ !D D P Œ !A
A D f 1; 2; 3g B D f 1; 2; 3gV 1 D 4 1 ! 2
2 D ! 1 C 2 C 3 3 D 2 ! 2 3
A BŒ !B D 3 1 C 4 2 C 3
D D f 1; 2; 3g F D f 1; 2; 3gV 1 D 2 1 ! 2 C 3
2 D 3 2 C 3 3 D !3 1 C 2 3
F DŒ !D D 1 ! 2 2 C 2 3
B D f 1; 2g C D f 1; 2gR2
B C C B
1 D"
75
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#1 D
"1
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#2 D
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2
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#1 D
"12
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"11
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44
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"84
#1 D
"22
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2
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#2 D
"42
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"42
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B C V
PC B
B CV D Rn C V P
C B
PB
PC B
V D R2 B D f 1; 2g C D f 1; 2gŒ 1 2 1 2 ! Œ I P !
P Œ !B D P Œ !C V
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B D f1 ! 2t C t 2; 3 ! 5t C 4t2; 2t C 3t2gC D f1; t; t 2g B
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B D f1 ! 3t2; 2 C t ! 5t2; 1 C 2tgt 2
B
V x1; : : : ; xn
D x1 1 C x2 2 C # # # C xn n
C
Œ !C D x1Œ 1!C C x2Œ 2!C C # # # C xnŒ n!C
Œ !C D%Œ 1 !C Œ 2 !C # # # Œ n !C
&264
x1:::
xn
375 .8/
PC B Œ !C D P
C B Œ !B V
Q
Œ !C D QŒ !B V .9/
D 1 Œ 1!CQ k D 2; : : : ; n
k QP
C B
B D f 0; : : : ; 6g C D f 0; : : : ; 6g kk t k kt
B CH D f 0; : : : ; 6g
P D%
Œ 0 !B # # # Œ 6 !B&
P "1
P "1 C0; : : : ; 6
t C
Z.5 3 t ! 6 4 t C 5 5 t ! 12 6 t/ dt .10/
P P "1
3
P D
24
1 2 !1!3 !5 0
4 6 1
35
1 D
24
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35
2 D
24
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35
3 D
24
!726
35
f 1; 2; 3g R3 Pf 1; 2; 3g
f 1; 2; 3g PC B
f 1; 2; 3g R3 Pf 1; 2; 3g f 1; 2; 3g
B D f 1; 2g C D f 1; 2g D D f 1; 2g
PC B
PD C
PD B
R2
P G PG P
PC B D
%Œ 1 !C Œ 2 !C
&D
"4 !61 1
#
PB C D . P
C B /!1 D 1
10
"1 6
!1 4
#D
":1 :6
!:1 :4
#
SS
fykg .:7/k 1k
.!1/k
yk = .7k
–2 –1 0 1 2 –2 –1 0 1 2 –2 0 2
yk = 1k yk = (–1)k
S
2k 3k k"2
3k k"2
ykC3 ! 2ykC2 C 9ykC1 ! 18yk D 0
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" !!7 2424 7
"
24
1 1 31 3 13 1 1
35
24
!2 !36 0!36 !23 0
0 0 3
35
24
3 !2 4!2 6 2
4 2 3
35
24
7 !4 4!4 5 0
4 0 9
35
2664
4 1 3 11 4 1 33 1 4 11 3 1 4
3775
2664
2 0 0 00 1 0 10 0 2 00 1 0 1
3775
A D
24
3 1 11 3 11 1 3
35 D
24
111
35
AA
A D
24
5 !4 !2!4 5 2!2 2 2
35
1 D
24
!221
35
2 D
24
110
35
1 2 AA
n " n
AT D A A D 3A D 4 ! D 0
n " n n
Rn T
B D T P T D P !1 DB
A n " n B n " mBTAB BTB BBT
A n " n A /! D!.A / ; Rn
AA!1
A BAB D BA AB
A D !1 P D! A k
! k D! k
A D PRP !1 P RA R
A
A
Rn B D T
Rn B B
B B2 D B
B
B n " n B2 B
Rn O D BD ! O
OW B
W W ?
BB
!.A ! !I /
2664
5 2 9 !62 5 !6 99 !6 5 2
!6 9 2 5
3775
2664
:38 !:18 !:06 !:04!:18 :59 !:04 :12!:06 !:04 :47 !:12!:04 :12 !:12 :41
3775
2664
:31 :58 :08 :44:58 !:56 :44 !:58:08 :44 :19 !:08:44 !:58 !:08 :31
3775
266664
10 2 2 !6 92 10 2 !6 92 2 10 !6 9
!6 !6 !6 26 99 9 9 9 !19
377775
.A2/T D .AA/T D ATAT AT D A
.A2/T D AA D A2 A2
A AA2
D P
Q. / D TA D T D D !1y21 C !2y2
2 C # # # C !ny2n
!1; : : : ;!n A PQ. /
¤!1; : : : ;!n
Q. / D 3x21 C 2x2
2 C x23 C 4x1x2 C 4x2x3
Positive definite
z
Indefinite
z
Negative definite
z
x1 x2
x1
x1x2
x2
A D
24
3 2 02 2 20 2 1
35
A !1 Q
AWEBTA
AA A D RTR R
A
A
WEB
TA A D!
5 1=31=3 1
"
D!
x1
x2
"D
!61
"D
!13
"
TA A D
24
4 3 03 2 10 1 1
35
D
24
x1
x2
x3
35 D
24
2!1
5
35 D
264
1=p
3
1=p
3
1=p
3
375
R2
10x21 ! 6x1x2 ! 3x2
2 5x21 C 3x1x2
R2
20x21 C 15x1x2 ! 10x2
2 x1x2
R3
8x21 C 7x2
2 ! 3x23 ! 6x1x2 C 4x1x3 ! 2x2x3
4x1x2 C 6x1x3 ! 8x2x3
R3
5x21 ! x2
2 C 7x23 C 5x1x2 ! 3x1x3
x23 ! 4x1x2 C 4x2x3
D Px2
1 C 10x1x2 C x22
P
A
9x21 C 7x2
2 C 11x23 ! 8x1x2 C 8x1x3
AP
D P TAP
D P
P
3x21 ! 4x1x2 C 6x2
2 9x21 ! 8x1x2 C 3x2
2
2x21 C 10x1x2 C 2x2
2 !5x21 C 4x1x2 ! 2x2
2
x21 ! 6x1x2 C 9x2
2 8x21 C 6x1x2
!2x21 ! 6x2
2 ! 9x23 ! 9x2
4 C 4x1x2 C 4x1x3 C 4x1x4 C6x3x4
4x21 C 4x2
2 C 4x23 C 4x2
4 C 3x1x2 C 3x3x4 ! 4x1x4 C4x2x3
x21 C x2
2 C x23 C x2
4 C 9x1x2 ! 12x1x4 C 12x2x3 C 9x3x4
11x21 ! x2
2 ! 12x1x2 ! 12x1x3 ! 12x1x4 ! 2x3x4
5x21 C 8x2
2 D .x1; x2/T D 1
x21 C x2
2 D 1
5x21 ! 3x2
2T D 1
n " n Rn
TAA
Q Q. / > 0Rn
ATA
AA D RTR R
k k2
A PD P TA
A 2 " 2TA D c c
A TA¤ A
Q. / D TA A D!
a bb d
"A ¤ 0
A
!1 !2 AA .A ! !I /
.! ! !1/.! ! !2/ !1 C !2 Da C d A !1!2 D A
Q A > 0 a > 0
Q A > 0 a < 0
Q A < 0
B m " n BTBB n " n BTB
n " n AB A D BTB
A D T P T D P !1
C D D C TC B D PCP T
B
A B n " nA C B
A n " nTA
TA!1
SG
D P
TA D T D D !1y21 C !2y
22 C # # # C !ny2
n
!iTA
D i i In
TAPositive semidefinite
z
x1 x2
Q. /
Rn
k k D 1; k k2 D 1; T D 1
x21 C x2
2 C # # # C x2n D 1
T D 1Q
Q. / T D 1
Q. / D 9x21 C 4x2
2 C 3x23
T D 1
x22 x2
3
4x22 % 9x2
2 3x23 % 9x2
3
Q. / D 9x21 C 4x2
2 C 3x23
% 9x21 C 9x2
2 C 9x23
D 9.x21 C x2
2 C x23/
D 9
x21 C x2
2 C x23 D 1 Q. /
Q. / D 9 D .1; 0; 0/Q. / T D 1
Q. /
9x21 $ 3x2
1; 4x22 $ 3x2
2
Q. / $ 3x21 C 3x2
2 C 3x23 D 3.x2
1 C x22 C x2
3/ D 3
x21 C x2
2 C x23 D 1 Q. / D 3 x1 D 0 x2 D 0 x3 D 1
Q. / T D 1
y
Parks andrecreation
1.4
4x2 + 9y2 = 36(indifference curves)
q (x, y) = 4q (x, y) = 3
q (x, y) = 2Road and bridge repair
2.1x
.2:1; 1:4/
x1 D x
3; x2 D y
2; ; x D 3x1 y D 2x2
x21 C x2
2 D 1
q.3x1; 2x2/ D .3x1/.2x2/ D 6x1x2 D!
x1
x2
"
Q. / D 6x1x2T D 1 Q. / D
TA
A D!
0 33 0
"
A ˙3
"1=
p2
1=p
2
#! D 3
"!1=
p2
1=p
2
#
! D !3 Q. / D q.x1; x2/ x1 D 1=p
2x2 D 1=
p2
x D 3x1 D3=
p2 & 2:1 y D 2x2 D
p2 & 1:4
q.x; y/ D 3.x; y/
Q. / D 3x21 C 3x2
2 C 2x1x2 Q
Q Q. /T D 1
D PTA TD
5x21 C 6x2
2 C 7x23 C 4x1x2 ! 4x2x3 D 9y2
1 C 6y22 C 3y2
3
3x21 C 2x2
2 C 2x23 C 2x1x2 C 2x1x3 C 4x2x3 D 5y2
1 C 2y22
y23
Q. /T D 1
Q. /T D 1 T D 0
Q. / D 5x21 C 6x2
2 C 7x23 C 4x1x2 ! 4x2x3
Q. / D 3x21 C 2x2
2 C 2x23 C 2x1x2 C 2x1x3 C 4x2x3
Q. / D 5x21 C 5x2
2 ! 4x1x2
Q. / D 7x21 C 3x2
2 C 3x1x2
Q. / D !2x21 ! x2
2 C 4x1x2 C 4x2x3
R3 Q. / T D 1
Q !1 !4
Q. / D 7x21 C x2
2 C 7x23 ! 8x1x2 ! 4x1x3 ! 8x2x3
R3 Q. /T D 1
Q !3
Q. / D 7x21 C 3x2
2 ! 2x1x2
x21 C x2
2 D 1
Q. / D !3x21 C 5x2
2 ! 2x1x2
x21 C x2
2 D 1
ATA
! Am % ! % M
m M! D TA
A n " n M m
TA 1
n tM m t D TA
t D .1 ! ˛/m C ˛M ˛D
p1 ! ˛ n C p
˛ 1T D 1 TA D t
x1x2 C 3x1x3 C 30x1x4 C 30x2x3 C 3x2x4 C x3x4
3x1x2 C 5x1x3 C 7x1x4 C 7x2x3 C 5x2x4 C 3x3x4
4x21 ! 6x1x2 ! 10x1x3 ! 10x1x4 ! 6x2x3 ! 6x2x4 ! 2x3x4
!6x21 ! 10x2
2 ! 13x23 ! 13x2
4 ! 4x1x2 ! 4x1x3 ! 4x1x4 C6x3x4
A D!
3 11 3
"
x
4
z
x1
x2
!""""""#""""""$
Q. /T D 1
"1=
p2
1=p
2
# "!1=
p2
1=p
2
#
D P P D"
1=p
2 !1=p
2
1=p
2 1=p
2
#
TD D 4y21 C 2y2
2
Q. /!1=
p2
1=p
2
" !10
"
TD Q. /
A D PDP !1
D A D QDP !1 m " nA
A A
A D U †V T ATWEB
A AT
!1 00 !3
" !!5 0
0 0
"
! p6 1
0p
6
" ! p3 2
0p
3
"
U
24
!1=3 2=3 2=32=3 !1=3 2=32=3 2=3 !1=3
35
U
264
1=p
6
!2=p
6
1=p
6
375
!!3 0
0 0
" !!2 0
0 !1
"
!2 !12 2
" !2 30 2
"
24
7 10 05 5
35
24
4 !22 !10 0
35
24
!3 16 !26 !2
35
24
1 10 1
!1 1
35
A D!
3 2 22 3 !2
"AT
A
AU V
A D
24
:40 !:78 :47:37 !:33 !:87
!:84 !:52 !:16
35
24
7:10 0 00 3:10 00 0 0
35
"
24
:30 !:51 !:81:76 :64 !:12:58 !:58 :58
35
A
AA AV
3 " 4A
A D
24
!:86 !:11 !:50:31 :68 !:67:41 !:73 !:55
35
24
12:48 0 0 00 6:34 0 00 0 0 0
35
"
2664
:66 !:03 !:35 :66!:13 !:90 !:39 !:13
:65 :08 !:16 !:73!:34 :42 !:84 !:08
3775
A m " nA D U †V T U m " m
† m " n rV n " n
AA!1
A j AjA
V ATAU AAT
† AATA AAT
A n " nA D T
A
P m " m PAA
A kA k1 1
A
U D Œ 1 # # # m " V D Œ 1 # # # n "
i i
A D #1 1T1 C #2 2
T2 C # # # C #r r
Tr :
ATj D #j j
1 % j % r D A
T W Rn ! Rm
B Rn C Rm
T B C m " n
A D
2664
!18 13 !4 42 19 !4 12
!14 11 !12 8!2 21 4 8
3775
A D
2664
6 !8 !4 5 !42 7 !5 !6 40 !1 !8 2 2
!1 !2 4 4 !8
3775
4 " 4
#1=#4
5 " 5
#1=#5
A D U †V T † m " n AT D .V T /T †T U T D V †T U T
AT V U †T n " m† †T A AT
A 2 " n AAT 2 " 2ATA
Rn
R8 8 " 300
N j R2
j w h
A n " n
A A
A A
A kA k D k kRn
TAP A
P n " nP T D P !1
TA > 0 TA
TA k k D 1A
TA A
D P P
P n " nD P TA
P !1
U m " n U U T
U
B m " n Rn kB k % #1
#1 B
m " n BB D P †Q P m " mQ n " n
† m " n
A n " n A ATA
f 1; : : : ; ng Rn
!1; : : : ;!n
A D !1 1T1 C # # # C !n n
Tn
A
!1; : : : ;!n A
A n " n rA A
r 1
A n " n
. A/? D A
Rn DO C O A A
n " n AA A
A n " nRn
n " n AA A D RTR
R
AA A D LU U
A m " n G D ATAA G
A
AA
n " n Gr G r " n
A GG G
BBT n " r B
n " n AA D PQ P n " n
A Q n " n
A D U †V T A D .U †U T /.UV T /
PP Q
m " n AA D UrDV T
r
AC D VrD!1U T
r
AC
Rm AAC
A
Rn ACAA
AACA D A ACAAC D AC
A DC D AC
A A DC D C
A DC A A
C A DA D
k Ck % k k D C
Rm AC
A D O OA
AA
ATAA D D .6; !1; !4; 6/
O OA A
kOk < kO C k
A D
2664
!3 !3 !6 6 1!1 !1 !1 1 !2
0 0 !1 1 !10 0 !1 1 !1
3775
A D
2664
4 0 !1 !2 0!5 0 3 5 0
2 0 !1 !2 06 0 !3 !6 0
3775
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