?±′?
1.?-1?t4?? ?6,
1 13
2 123
3123
2
232
45
x yy
x yyy
xyyy
=+?
=?++?
= ++?
,
1 12
2 13
3 23
3
2
3
y zz
y zz
yzz
=?+?
=+?
=?+?
,"￠ 123,,zzz 123,,xxx
,X4?? ?6,
·?+?-1 ?k?
1111
2222
3333
11
22
33
201 310
2 3 2 2 0 1
4 15 0 13
201 310 613
232 2 01 12 49
4 1 5 0 1 3 10
xyyz
xyyz
xz
=?=
=? =?
g
è
1
2
31 16
z
z
z
2.A?
1 11 121
111,13 1
1 11 214
=? =?
ABè" 1? 2?ABA 2?22?AB
3?()()+?ABAB 4AB BA 5?TAB
·? 1)
1 11 121 1 11
2 111 13 1 2111
1 11 21 4 1 11
=? ×
ABA
464 2 2 2 242
222 2 2 2 400
206 2 22 024
==
2)
22
22
1 11 121
111 13 1
1 11 214
=
AB
113 593 4 80
1 1 1 2 10 6 3 11 7
311 739 448
==
3)
232 0 10 8120
(+)( )040 222 888
3 0 5 1 2 3 5 13 15
= =
ABAB
4)
464 024 440
222 353 5 31
206 517 311
= =
AB BA
5) T
1 11121 222
=11 1131 044
11 1214 464
=?
AB
3êAu1kAu1k-?L ,X,/?
1?
4317
1 232
5701
·?
4 3 1 7 4 7 3 2 1 1 35
123217(2)2316
5 7 0 1 5 7 7 2 0 1 49
×+×+×
=×+?×+×=
×+×+×
2?( )
3
1232
1
·? ( )
3
1 2 3 2 (1 3 2 2 3 1) (10)
1
=×+×+×=
3? ( )
1
132 10
2
3
·? ( )
1 3 2 10
1 3 21032 10
2 6 2 20
3 9 6 30
=?
4?
131
21400 12
1 1341 31
402
·?
131
2140 0 12 6 78
1134131 2056
402
=
5? ( )
11 12 13 1
1 2 3 21 22 23 2
31 32 33 3
aaax
xxxaaax
aaax
·?
( )
( )
11 12 13 1
1 2 3 12 22 23 2
313 23 33
1
11 1 12 2 13 3 12 1 22 2 23 3 13 1 23 2 33 3 2
3
222
11 1 22 2 33 3 12 1 2 13 1 3 23 2 3222
aaa x
xxxaaax
xaaa
x
axaxaxaxaxaxaxaxax x
x
a x a x a x a xx a xx a xx
=++ ++ ++×
=+++++
6?
11 12 13
21 22 23
31 32 33
010
100
001
aaa
aaa
aaa
·?
11 12 13 21 22 23
21 22 23 11 12 13
31 32 33 31 32 33
010
100
001
aaa aaa
aaa aaa
aaa aaa
=
7?
11 12 13
21 22 23
31 32 33
100
010
00
aaa
aaa
aak
·?
11 12 13 11 12 13
21 22 23 21 22 23
31 32 33 31 32 33
100
010
00
a a a a a ka
aaa aaka
aaa k aaka
=
8)
12101031
01010121
002100 23
00030003
·?
1210 10 3 1 12 5 2
0101 01 2 1 01 2 4
0021 00 23 00 43
00030003 0009
=
9)
11 12 13
21 22 23
31 32 33
100
010
01
aaa
aaa
aaak
·?
11 12 13 11 13 12 13
21 22 23 21 23 22 23
31 32 33 31 33 32 33
100
010
01
aaa akaaa
aaa akaaa
aaak akaaa
+
=+
+
4.A?
10
01
00
k
k
k
=
A è" 23,AA.JA?a
12
1
( 1)
2
0
00
nnn
n nn
n
nnkkk
k nk
k
=
A
·?
2
22
2110 10
0101 0 2
00 00 00
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λ λ λλ
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==
ù
32
32 32
3
33
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00
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λλ
λ
=?=
A AA
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12
1
( 1)
2
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k kk
k
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12 111
1 1
1
( 1) ( 1)( 1)
1022
0 0 1 0 ( 1)
0000 00
kkk kkk
kk
kk
kk kk
A
λλλ λλλλ
λλλ
+
+ +?
+
+
=?= =+
+D:&4?"? s)ú-1,
12
1
( 1)
2
0
00
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n nn
n
nnn
An
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λ
=
5.A? A? B n L
?L èè Aí/?-?L èA?a TB AB3 í/?-?L ,
A?a? ′ T =AAè1 TTTTTTT( ) ()==BAB BA B BAB
6.A? A? BF? n L
í/?-?L èA?a AB í/?-?L ,X?U 5ê =AB BA.
A?a? ′ TT,==AABB
ú?? TTT()=?==AB BA AB B A AB
GAB í/?-?L ,
U?? T T TT() ()=?= ==AB AB AB AB B A BA.
7.A? A n L
í/?-?L èè 2 =AOèA?a =AO
·?A? ()ij nna ×=A è+b T =AAè 2 =AOè1
2
1
1
2
2
12T2
1
0( 1,2,...,)
n
nj
ijn
j
ij
j
n
nj
j
a
a
ain
a
a
=
=
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=
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= = =? ==
∑
∑
∑
AAO
0 (,1,2,...,)ijaijn? = =?=AO
8."?-?L ,XEú-?L
1) 1225
2)
123
012
001
3)
121
342
5 41
4)
1000
1200
2130
1214
·
(1) 1225=A 1=A
11 21 12 225,2 ( 1),2 ( 1),1= = ×? = ×? =AAAA
11 21
12 22
52
21
==
AAA
AA ?
1 1 52
21
==
AAA
(2)
123
0 1 2 | | =1
001
=
èAA
11 12 13 21 22 23 31 32 331 0 0 2 1 0 7 2 1== = =?== = =?=AAAA AAAA A
? 1
1 271
012
001
==?
AAA
(3)
121
3 4 2 | |2
5 41
=?=
èAA
11 21 31 12 22 32
13 23 33
4 2 0 13 6 1
32 14 2
=? = = =? = =?
=? = =?
A AAA AA
A AA
1
210
1 1313
22
1671
==
AAA
(4) 21 31 41 32 42 43
1000
1200 |24 0
2130
1214
= = ======
A A AAAAAA
11 22 33 4424 12 8 6= = ==A A AA
3
12
100
( 1) 2 3 0 12
114
=? =?A 413
120
( 1) 2 1 0 12
124
=? =?A 514
120
(1)2133
121
=?=A
5
23
100
(1)2104
124
=? =?A 624
100
(1)2135
121
=? =?A 734
100
(1)1202
121
=? =?A
? 1
1 0 00
11 00
221
1110
263
1 5 11
8 24 12 4
==
AAA
9."?·??/? (4? )
1) 25 4613 21=
X
·?
125 46 3 546 223
13 21 12 21 0 8
===X
2)
2 1 1 1 13
21 0 432
1 11 1 25
=
X
·?
11 13 2 1 1 1 13 1 0 1
1432 21 0 432 23 2=
31 25 1 11 1 25 33 0
= =
X
3)
010 100 1 4 3
100 001 201
001 010 1 20
=?
X
·?
11010 1 4 3 100 010 1 4 3 100
100 2 0 1 001 100 2 0 1 001
001 1 2 0 010 001 1 2 0 010
=?=?
X
2 10
=134
102
4)
123
123
1 23
231
2252
353
xxx
xxx
x xx
++=?
++=?
+ +=?
·?
1231
252
3513
=
X ?
112311
22520
35130
==
X
10.A? ()k k=AO!7H D èA?a 1 21( ),.,k = ++ ++EAEAAA
A?? 21( )(,.,)k ++ ++EAEAAA
2121..,(,.,)k kk=++++?+++ +=EAA A AA AAE
1? 1 21( ),.,k = ++ ++EAEAAA
11.A? n L
?L A$μC?G2?? 12121..,( 0)kkk kkkαα ααα+++++=≠A A A A EO èJ
121,,...,,kkαα αα?F? rDèA?a? A M2?-?L èJmW,XEú-?L ,
A?? ′ 12121..,( 0)kkk kkkαα ααα+++++=≠A A A A EO
1 12321(,.,)kkk kkαα αα+ + + + =?AAAE
G 123211(,.,)kkk k
k
αααα+ + ++=?AAAE
1 123211(,.,)kkk k
k
αααα=? + + ++A AAA
12,A? n L
?L A$μC?G2?? 2 32=A A EO,A?a A ?EúèJ"JEú-?L ,
A?? ′ 2213 2 3 2 ( 3)2===AAEOAAE AAEE
1 A ?Eúè 1 1 ( 3)2? =?A AE
13.A? n L
?L A? B$μC? +=A B ABèA?a?
1)?AE ?Eú× 2)81
1 30
210
002
=
B è" A
A?? 1) ′ ()+ =? + = =?ABAB ABABE E AE AEB E
1 ()()=AEBEEè G?AEa?BE
?Eúèèf ?Eú-?L
2) 1() ()?+==?=?ABABABEBABBE
1
0 30 0 301
2 0 0 ( ) 2006
0 0 1 0 06
= =?
BE BE
1 30 030 63011
( ) 2 1 0 200 26 066
002006 0012
=?=? =?
ABBE
14.A? 1T1
12 3 2 1201
01 2 3 0120,,(2)
00 1 2 0010
00 0 1 0001
= =?=
B C ECBACè" A
·?A? 12 12
12
12 3 2 1201
01 2 3 0120,
00 1 2 0010
00 0 1 0001
= ===
BB BCBC
OB OE
J
11
11 12
2
=
B BCC
OE
11 11
1 121 12 2 12 121
121
==
BBB BC E BB BCBCB
OBOE OB
112
01
=
B è112 1 2 3 2 740123 23==
BB
1
1 21
120112411247
012001200124
= ==
BCB
11
12 121
3 11
07
=
B B BCB
11
12 12 121
1
1 0 3 11
0107
0012
0001
==
E B B BCBCB
OB
1 23
1
1
1 0 3 11
01072
0012
000 1
==
EBECB
B
1 11111
T 1 11 2 31 1 1 2 311 12
2
(2)
===
E BB B B C BBB BCA ECBC
OEOB OB
5à
11
1 2 31
1 2 0 1 3 11 1 2 4 1 3 17 1 16
01200701 2007 27
= = =
B C BB
T
1 2 1 16 1 0 00
0 1 2 7 2 1 00
0 0 1 2 1 210
0 0 0 1 16 721
==
AA G
15êA? 1 111002==
PAP P A 1 4èJ è è"11,
·? 1? =P AP 1?=AP P 1 11 11 1?=AP P
3=P 1411=P 1 1 14113=P
5à
11
11
11
1010
02 02
==
11 11
14
101 4 2731 273233
1 1 1 1 683 68402
33
==
A
16.A? m??NM? 2012( ),.,mmfx a ax ax ax= + + ++ èA?
2
012( ),..
m
mfaaaa= + + ++AEAAAè()fA/??L A,X m??NM??A?
1) 2()1fx xx=++ è
101
130
214
=
A
2) 2() 32fx xx=?++è 2003=
A
A?" ()f A
·? 1)
2
2
100 101 101
() 010 130 130
001 214 214
f
=+=++
A EAA
201 315 516
140 491 5131
2 1 5 11 7 18 13 8 23
=+=
2)
2
2 10 20 20()32 32
01 03 03f
=?++=?++
A E AA
30 40 40 50
0 3 0 6 0 9 0 12
= ++=
17.A? n L
-?L A,XLc-?L *A èA?a *1| |||n?=AA
A?a?' | |0≠A êèE-ê-?L A ?Eúèè * ||=AA AE
1 Y? * *1||| ||| | |||nn?=?=AAA AA
'=AOêè '
Y * =AO
QNl?0?×
' |0≠=AOA | êè? Y *| |0=A èV81á'
èE-ê *A ?Eúè
í * *1 *1() ||()===AAAAEAOE-a ≠AO-ˉ,òè' |0≠=AOA | ê
Y *| |0=A
18êA? 1001==?==
AB CD èP`A? ≠ ABAB CDCD
?P`,
1 0 10 2 0 00
0 1 01 0 2 00 2010 4
10 10 10 10 0201
0 101 0 101
====ABCD
5à 11 011==ABCD
≠ABABCD CD
19.A? 42
34
43,
20
22
=
O
A AA
O
" ?
·?
34
43
20
22
O
O
=
A è? 1 3443=A 2 2022=A
í 1
2
O
O
=
AA
A
8 8
8 11
8
2 2
OO
OO
==
AAAAA
888 8 8 16
12 1210===AAAAA
4
4 4
4 1
44
2
64
50
05
20
22
OO
O O
==
AA
A
20.A? n L
-?L A ? s L
-?L BF? ?Eúè" (1)
1
OA
BO è(2)
1
AO
CB
·? (1)A?
1
12
34
=CCOA CCBO
J 1C sn× -?L ,2C ss× -?L è 3C nn× -?L ,4C ns× -?L
í 12
34
nnn
sss×
==
OA EOCC E
CCB O OE
1?
1
33
1
44
1
11
1
22
()
()
n
s
=?=
=?=
=?=?
=?=?
, ü
, ü
ACE CA
ACOCOA
BCOCOB
BCE CB
1 1
1
=
OA OBBO AOê
(2)A?
1
12
34
=CCAO CCCB è
J 1C nn× -?L ,2C ns× -?L è 3C sn× -?L ,4C ss× -?L
í 12
34
n
s
==
EOCCAO E
CCCB OE
1?
1
11
1
22
111
133
1
244
()
()
n
s
=?=
=?=
+ =? =
+ =?=?
ACE CA
ACOCOA
CC BC O C B CA B
CC BC E C B
, ü
, ü
1 1
111
=
AO AOCB BCABê
21êA? A 3 L
-?L è 1||2=A è" 1*|(2) 5|AA
·? ′ 1||2=A è1-?L A ?Eúèè 1 * * * 31112,| |||||4= = ==A AAAAA
? 1* 1*** 3*1|(2) 5|| 5|| 5|(4)| |162=?=?=? =?AAAAAAA
22êA?-?L A ?EúèA?aJLc-?L *A 3 ?Eúèè * 1 1*() ()=AA
A?a?+b A ?Eúèè * *1|| ||?=?=AA AE A AAè1 *A ?Eú
*1 1()
||
=AA
A è
1 1* 1 1*11()()| | ()
|| ||
= =?=AAAEEAA
AA
23êA?
0 33
10,2
123
= =+
A ABABèè" B
·? 2 ( 2)=+=ABA B A EBA
5à
0 33 100 2 3 3
2 110 2010 1 10,| 2|20
123 001 121
=? = =≠
AE AE
1 1
13 3 0 33 200 10011
( 2) 11 3 1 10 020 01022
1 1 1 123 002 001
=?=? ==
B AEA
24êA? 2
101
0 2 0,
101
= +=+
A ABEABè è" B
·? 22() ()()()+=+ = =? +AB E A B A EB A E A EB A E A E
5à
101 1 001
0 2 0 1 0 1 0,
101 1 100
=? =?≠
AE AEè | |= 1 0
1
101 1 201
020 1 030
101 1 102
=+=+=
BAE
25êA? *(1,2,1),28diag=? =?A A BA BA E è" B
·? * * *12 8 ( 2) 8 8( 2)?= = =A BA BA E A E BA E BA A E
* 118( 2)=B A EA
5à*1*
24
| 1,21?
= =?=?
AAA AE
* 11
1 1
24 1
8(2)8142
12
4
= = =?
B A EA
26ê?-1-?L A,XLc-?L * 11
1 0 00
0 1 00,3
1 0 10
0 308
= =+
A ABA BA Eè" B
·? * * *1
1 0 00
0 1 00,| |8||2,||()
1 0 10
0 308
= =?==
A A A AAA
A?* 1 1 0 10,,,1 0 3 08= ===EOA ECDCDJ
*1
11
1 000 2 000
0 100 0 200(),
1010 2020
0 38 0 18 0 34 0 14
===
EOAA
DCD
? 11 1 113() 3 3()= + =? =?ABA BA E A E BA E BA A E
1 1
1000 2 000 600 0
0100 0 200 060 0
3()32010 2020 606 0
4 310101010 00
3 44
===
B AEA
27êA?
1
1
5
==
AP P P
111
èJ =1 0 2è
1 11
è
" 82()(56)? =?+A A E AA
·?? 11kk=?=?=AP P A P P A P P
1 828 81( ) (5 6 ) ( 5 )( ) ( 5 )( )=?+==A A E AA AA EAE P (EP
8
1
1 1 1 11
5
5 5 1 51
PP=
162
40
045
11 1 11 1
=10 2 10 2
1 11 1 11
112 111
0 4111
0 111
=
11 1 11 1
= 1 0 2 1 0 2
1 11 1 11
·`?
8 289101() (5 6 ) 5 6 ()=?+=? +=A AE AA A A A PP
5à
( 1) 12
()(1)0
(5)0
==
1
1
12 111
( ) ( ) 0 4111
0 111
=
A P P
111 111
= 1 0 2 1 0 2
1 11 1 11
28êA?-?L A? B
` A+BF? ?EúèA?a 11+AB3 ?EúèJ"JEú-?L ?
A?a? ′ 11111( )()( )()+ + = ++A BBABAABEABA
1 11()()= ++ ==ABAABAAAE
1 11+AB3 ?Eúèè 111()+=+A B BABAê111()+=+A B AABB
29êAu1k
12101031
01010121
0021 00 23
0003 00 0 3
·?
12101031
01010121
0021 00 23
0003 00 0 3
+==
AEEC AACD
O B O D O BD
1231 23 52
0121 0 3 24
21 23 43
0303 09
+= +=
==
ACD
BD
1?
12101031 1252
0101 01 2 1 01 2 4
0021 00 2 3 00 4 3
00030003 0009
=
30ê"?-?L ,XEú-?L
? 1?
5200
2100
0083
0052
? 2?
1000
1200
2130
1214
·? (1)A?
5200
2100 52 83,,
0083 21 52
0052
= ==
AO AB
OB
1?
1
1
1
5200 1 200
2100 2500
0083 0023
0052 0 0 5 8
==
AO
OB
(2)A?
1000
1200 10 21 30,,,
2130 12 12 14
1214
= ===
AO ABC
BC
1
1
111
10 00
111000 00
221200
1112130 0
2631214
15 11
8 24 12 4
==
AO
CBAC
1.?-1?t4?? ?6,
1 13
2 123
3123
2
232
45
x yy
x yyy
xyyy
=+?
=?++?
= ++?
,
1 12
2 13
3 23
3
2
3
y zz
y zz
yzz
=?+?
=+?
=?+?
,"￠ 123,,zzz 123,,xxx
,X4?? ?6,
·?+?-1 ?k?
1111
2222
3333
11
22
33
201 310
2 3 2 2 0 1
4 15 0 13
201 310 613
232 2 01 12 49
4 1 5 0 1 3 10
xyyz
xyyz
xz
=?=
=? =?
g
è
1
2
31 16
z
z
z
2.A?
1 11 121
111,13 1
1 11 214
=? =?
ABè" 1? 2?ABA 2?22?AB
3?()()+?ABAB 4AB BA 5?TAB
·? 1)
1 11 121 1 11
2 111 13 1 2111
1 11 21 4 1 11
=? ×
ABA
464 2 2 2 242
222 2 2 2 400
206 2 22 024
==
2)
22
22
1 11 121
111 13 1
1 11 214
=
AB
113 593 4 80
1 1 1 2 10 6 3 11 7
311 739 448
==
3)
232 0 10 8120
(+)( )040 222 888
3 0 5 1 2 3 5 13 15
= =
ABAB
4)
464 024 440
222 353 5 31
206 517 311
= =
AB BA
5) T
1 11121 222
=11 1131 044
11 1214 464
=?
AB
3êAu1kAu1k-?L ,X,/?
1?
4317
1 232
5701
·?
4 3 1 7 4 7 3 2 1 1 35
123217(2)2316
5 7 0 1 5 7 7 2 0 1 49
×+×+×
=×+?×+×=
×+×+×
2?( )
3
1232
1
·? ( )
3
1 2 3 2 (1 3 2 2 3 1) (10)
1
=×+×+×=
3? ( )
1
132 10
2
3
·? ( )
1 3 2 10
1 3 21032 10
2 6 2 20
3 9 6 30
=?
4?
131
21400 12
1 1341 31
402
·?
131
2140 0 12 6 78
1134131 2056
402
=
5? ( )
11 12 13 1
1 2 3 21 22 23 2
31 32 33 3
aaax
xxxaaax
aaax
·?
( )
( )
11 12 13 1
1 2 3 12 22 23 2
313 23 33
1
11 1 12 2 13 3 12 1 22 2 23 3 13 1 23 2 33 3 2
3
222
11 1 22 2 33 3 12 1 2 13 1 3 23 2 3222
aaa x
xxxaaax
xaaa
x
axaxaxaxaxaxaxaxax x
x
a x a x a x a xx a xx a xx
=++ ++ ++×
=+++++
6?
11 12 13
21 22 23
31 32 33
010
100
001
aaa
aaa
aaa
·?
11 12 13 21 22 23
21 22 23 11 12 13
31 32 33 31 32 33
010
100
001
aaa aaa
aaa aaa
aaa aaa
=
7?
11 12 13
21 22 23
31 32 33
100
010
00
aaa
aaa
aak
·?
11 12 13 11 12 13
21 22 23 21 22 23
31 32 33 31 32 33
100
010
00
a a a a a ka
aaa aaka
aaa k aaka
=
8)
12101031
01010121
002100 23
00030003
·?
1210 10 3 1 12 5 2
0101 01 2 1 01 2 4
0021 00 23 00 43
00030003 0009
=
9)
11 12 13
21 22 23
31 32 33
100
010
01
aaa
aaa
aaak
·?
11 12 13 11 13 12 13
21 22 23 21 23 22 23
31 32 33 31 33 32 33
100
010
01
aaa akaaa
aaa akaaa
aaak akaaa
+
=+
+
4.A?
10
01
00
k
k
k
=
A è" 23,AA.JA?a
12
1
( 1)
2
0
00
nnn
n nn
n
nnkkk
k nk
k
=
A
·?
2
22
2110 10
0101 0 2
00 00 00
λλλλ
λ λ λλ
λλ λ
==
ù
32
32 32
3
33
03
00
λλλ
λλ
λ
=?=
A AA
A? nk= êè
12
1
( 1)
2
0 ( 2)
00
kkk
k kk
k
kkk
kk
λλλ
λλ
λ
=≥
A ?0??
í' 1nk=+ê?
12 111
1 1
1
( 1) ( 1)( 1)
1022
0 0 1 0 ( 1)
0000 00
kkk kkk
kk
kk
kk kk
A
λλλ λλλλ
λλλ
+
+ +?
+
+
=?= =+
+D:&4?"? s)ú-1,
12
1
( 1)
2
0
00
nnn
n nn
n
nnn
An
λλλ
λλ
λ
=
5.A? A? B n L
?L èè Aí/?-?L èA?a TB AB3 í/?-?L ,
A?a? ′ T =AAè1 TTTTTTT( ) ()==BAB BA B BAB
6.A? A? BF? n L
í/?-?L èA?a AB í/?-?L ,X?U 5ê =AB BA.
A?a? ′ TT,==AABB
ú?? TTT()=?==AB BA AB B A AB
GAB í/?-?L ,
U?? T T TT() ()=?= ==AB AB AB AB B A BA.
7.A? A n L
í/?-?L èè 2 =AOèA?a =AO
·?A? ()ij nna ×=A è+b T =AAè 2 =AOè1
2
1
1
2
2
12T2
1
0( 1,2,...,)
n
nj
ijn
j
ij
j
n
nj
j
a
a
ain
a
a
=
=
=
=
=
= = =? ==
∑
∑
∑
AAO
0 (,1,2,...,)ijaijn? = =?=AO
8."?-?L ,XEú-?L
1) 1225
2)
123
012
001
3)
121
342
5 41
4)
1000
1200
2130
1214
·
(1) 1225=A 1=A
11 21 12 225,2 ( 1),2 ( 1),1= = ×? = ×? =AAAA
11 21
12 22
52
21
==
AAA
AA ?
1 1 52
21
==
AAA
(2)
123
0 1 2 | | =1
001
=
èAA
11 12 13 21 22 23 31 32 331 0 0 2 1 0 7 2 1== = =?== = =?=AAAA AAAA A
? 1
1 271
012
001
==?
AAA
(3)
121
3 4 2 | |2
5 41
=?=
èAA
11 21 31 12 22 32
13 23 33
4 2 0 13 6 1
32 14 2
=? = = =? = =?
=? = =?
A AAA AA
A AA
1
210
1 1313
22
1671
==
AAA
(4) 21 31 41 32 42 43
1000
1200 |24 0
2130
1214
= = ======
A A AAAAAA
11 22 33 4424 12 8 6= = ==A A AA
3
12
100
( 1) 2 3 0 12
114
=? =?A 413
120
( 1) 2 1 0 12
124
=? =?A 514
120
(1)2133
121
=?=A
5
23
100
(1)2104
124
=? =?A 624
100
(1)2135
121
=? =?A 734
100
(1)1202
121
=? =?A
? 1
1 0 00
11 00
221
1110
263
1 5 11
8 24 12 4
==
AAA
9."?·??/? (4? )
1) 25 4613 21=
X
·?
125 46 3 546 223
13 21 12 21 0 8
===X
2)
2 1 1 1 13
21 0 432
1 11 1 25
=
X
·?
11 13 2 1 1 1 13 1 0 1
1432 21 0 432 23 2=
31 25 1 11 1 25 33 0
= =
X
3)
010 100 1 4 3
100 001 201
001 010 1 20
=?
X
·?
11010 1 4 3 100 010 1 4 3 100
100 2 0 1 001 100 2 0 1 001
001 1 2 0 010 001 1 2 0 010
=?=?
X
2 10
=134
102
4)
123
123
1 23
231
2252
353
xxx
xxx
x xx
++=?
++=?
+ +=?
·?
1231
252
3513
=
X ?
112311
22520
35130
==
X
10.A? ()k k=AO!7H D èA?a 1 21( ),.,k = ++ ++EAEAAA
A?? 21( )(,.,)k ++ ++EAEAAA
2121..,(,.,)k kk=++++?+++ +=EAA A AA AAE
1? 1 21( ),.,k = ++ ++EAEAAA
11.A? n L
?L A$μC?G2?? 12121..,( 0)kkk kkkαα ααα+++++=≠A A A A EO èJ
121,,...,,kkαα αα?F? rDèA?a? A M2?-?L èJmW,XEú-?L ,
A?? ′ 12121..,( 0)kkk kkkαα ααα+++++=≠A A A A EO
1 12321(,.,)kkk kkαα αα+ + + + =?AAAE
G 123211(,.,)kkk k
k
αααα+ + ++=?AAAE
1 123211(,.,)kkk k
k
αααα=? + + ++A AAA
12,A? n L
?L A$μC?G2?? 2 32=A A EO,A?a A ?EúèJ"JEú-?L ,
A?? ′ 2213 2 3 2 ( 3)2===AAEOAAE AAEE
1 A ?Eúè 1 1 ( 3)2? =?A AE
13.A? n L
?L A? B$μC? +=A B ABèA?a?
1)?AE ?Eú× 2)81
1 30
210
002
=
B è" A
A?? 1) ′ ()+ =? + = =?ABAB ABABE E AE AEB E
1 ()()=AEBEEè G?AEa?BE
?Eúèèf ?Eú-?L
2) 1() ()?+==?=?ABABABEBABBE
1
0 30 0 301
2 0 0 ( ) 2006
0 0 1 0 06
= =?
BE BE
1 30 030 63011
( ) 2 1 0 200 26 066
002006 0012
=?=? =?
ABBE
14.A? 1T1
12 3 2 1201
01 2 3 0120,,(2)
00 1 2 0010
00 0 1 0001
= =?=
B C ECBACè" A
·?A? 12 12
12
12 3 2 1201
01 2 3 0120,
00 1 2 0010
00 0 1 0001
= ===
BB BCBC
OB OE
J
11
11 12
2
=
B BCC
OE
11 11
1 121 12 2 12 121
121
==
BBB BC E BB BCBCB
OBOE OB
112
01
=
B è112 1 2 3 2 740123 23==
BB
1
1 21
120112411247
012001200124
= ==
BCB
11
12 121
3 11
07
=
B B BCB
11
12 12 121
1
1 0 3 11
0107
0012
0001
==
E B B BCBCB
OB
1 23
1
1
1 0 3 11
01072
0012
000 1
==
EBECB
B
1 11111
T 1 11 2 31 1 1 2 311 12
2
(2)
===
E BB B B C BBB BCA ECBC
OEOB OB
5à
11
1 2 31
1 2 0 1 3 11 1 2 4 1 3 17 1 16
01200701 2007 27
= = =
B C BB
T
1 2 1 16 1 0 00
0 1 2 7 2 1 00
0 0 1 2 1 210
0 0 0 1 16 721
==
AA G
15êA? 1 111002==
PAP P A 1 4èJ è è"11,
·? 1? =P AP 1?=AP P 1 11 11 1?=AP P
3=P 1411=P 1 1 14113=P
5à
11
11
11
1010
02 02
==
11 11
14
101 4 2731 273233
1 1 1 1 683 68402
33
==
A
16.A? m??NM? 2012( ),.,mmfx a ax ax ax= + + ++ èA?
2
012( ),..
m
mfaaaa= + + ++AEAAAè()fA/??L A,X m??NM??A?
1) 2()1fx xx=++ è
101
130
214
=
A
2) 2() 32fx xx=?++è 2003=
A
A?" ()f A
·? 1)
2
2
100 101 101
() 010 130 130
001 214 214
f
=+=++
A EAA
201 315 516
140 491 5131
2 1 5 11 7 18 13 8 23
=+=
2)
2
2 10 20 20()32 32
01 03 03f
=?++=?++
A E AA
30 40 40 50
0 3 0 6 0 9 0 12
= ++=
17.A? n L
-?L A,XLc-?L *A èA?a *1| |||n?=AA
A?a?' | |0≠A êèE-ê-?L A ?Eúèè * ||=AA AE
1 Y? * *1||| ||| | |||nn?=?=AAA AA
'=AOêè '
Y * =AO
QNl?0?×
' |0≠=AOA | êè? Y *| |0=A èV81á'
èE-ê *A ?Eúè
í * *1 *1() ||()===AAAAEAOE-a ≠AO-ˉ,òè' |0≠=AOA | ê
Y *| |0=A
18êA? 1001==?==
AB CD èP`A? ≠ ABAB CDCD
?P`,
1 0 10 2 0 00
0 1 01 0 2 00 2010 4
10 10 10 10 0201
0 101 0 101
====ABCD
5à 11 011==ABCD
≠ABABCD CD
19.A? 42
34
43,
20
22
=
O
A AA
O
" ?
·?
34
43
20
22
O
O
=
A è? 1 3443=A 2 2022=A
í 1
2
O
O
=
AA
A
8 8
8 11
8
2 2
OO
OO
==
AAAAA
888 8 8 16
12 1210===AAAAA
4
4 4
4 1
44
2
64
50
05
20
22
OO
O O
==
AA
A
20.A? n L
-?L A ? s L
-?L BF? ?Eúè" (1)
1
OA
BO è(2)
1
AO
CB
·? (1)A?
1
12
34
=CCOA CCBO
J 1C sn× -?L ,2C ss× -?L è 3C nn× -?L ,4C ns× -?L
í 12
34
nnn
sss×
==
OA EOCC E
CCB O OE
1?
1
33
1
44
1
11
1
22
()
()
n
s
=?=
=?=
=?=?
=?=?
, ü
, ü
ACE CA
ACOCOA
BCOCOB
BCE CB
1 1
1
=
OA OBBO AOê
(2)A?
1
12
34
=CCAO CCCB è
J 1C nn× -?L ,2C ns× -?L è 3C sn× -?L ,4C ss× -?L
í 12
34
n
s
==
EOCCAO E
CCCB OE
1?
1
11
1
22
111
133
1
244
()
()
n
s
=?=
=?=
+ =? =
+ =?=?
ACE CA
ACOCOA
CC BC O C B CA B
CC BC E C B
, ü
, ü
1 1
111
=
AO AOCB BCABê
21êA? A 3 L
-?L è 1||2=A è" 1*|(2) 5|AA
·? ′ 1||2=A è1-?L A ?Eúèè 1 * * * 31112,| |||||4= = ==A AAAAA
? 1* 1*** 3*1|(2) 5|| 5|| 5|(4)| |162=?=?=? =?AAAAAAA
22êA?-?L A ?EúèA?aJLc-?L *A 3 ?Eúèè * 1 1*() ()=AA
A?a?+b A ?Eúèè * *1|| ||?=?=AA AE A AAè1 *A ?Eú
*1 1()
||
=AA
A è
1 1* 1 1*11()()| | ()
|| ||
= =?=AAAEEAA
AA
23êA?
0 33
10,2
123
= =+
A ABABèè" B
·? 2 ( 2)=+=ABA B A EBA
5à
0 33 100 2 3 3
2 110 2010 1 10,| 2|20
123 001 121
=? = =≠
AE AE
1 1
13 3 0 33 200 10011
( 2) 11 3 1 10 020 01022
1 1 1 123 002 001
=?=? ==
B AEA
24êA? 2
101
0 2 0,
101
= +=+
A ABEABè è" B
·? 22() ()()()+=+ = =? +AB E A B A EB A E A EB A E A E
5à
101 1 001
0 2 0 1 0 1 0,
101 1 100
=? =?≠
AE AEè | |= 1 0
1
101 1 201
020 1 030
101 1 102
=+=+=
BAE
25êA? *(1,2,1),28diag=? =?A A BA BA E è" B
·? * * *12 8 ( 2) 8 8( 2)?= = =A BA BA E A E BA E BA A E
* 118( 2)=B A EA
5à*1*
24
| 1,21?
= =?=?
AAA AE
* 11
1 1
24 1
8(2)8142
12
4
= = =?
B A EA
26ê?-1-?L A,XLc-?L * 11
1 0 00
0 1 00,3
1 0 10
0 308
= =+
A ABA BA Eè" B
·? * * *1
1 0 00
0 1 00,| |8||2,||()
1 0 10
0 308
= =?==
A A A AAA
A?* 1 1 0 10,,,1 0 3 08= ===EOA ECDCDJ
*1
11
1 000 2 000
0 100 0 200(),
1010 2020
0 38 0 18 0 34 0 14
===
EOAA
DCD
? 11 1 113() 3 3()= + =? =?ABA BA E A E BA E BA A E
1 1
1000 2 000 600 0
0100 0 200 060 0
3()32010 2020 606 0
4 310101010 00
3 44
===
B AEA
27êA?
1
1
5
==
AP P P
111
èJ =1 0 2è
1 11
è
" 82()(56)? =?+A A E AA
·?? 11kk=?=?=AP P A P P A P P
1 828 81( ) (5 6 ) ( 5 )( ) ( 5 )( )=?+==A A E AA AA EAE P (EP
8
1
1 1 1 11
5
5 5 1 51
PP=
162
40
045
11 1 11 1
=10 2 10 2
1 11 1 11
112 111
0 4111
0 111
=
11 1 11 1
= 1 0 2 1 0 2
1 11 1 11
·`?
8 289101() (5 6 ) 5 6 ()=?+=? +=A AE AA A A A PP
5à
( 1) 12
()(1)0
(5)0
==
1
1
12 111
( ) ( ) 0 4111
0 111
=
A P P
111 111
= 1 0 2 1 0 2
1 11 1 11
28êA?-?L A? B
` A+BF? ?EúèA?a 11+AB3 ?EúèJ"JEú-?L ?
A?a? ′ 11111( )()( )()+ + = ++A BBABAABEABA
1 11()()= ++ ==ABAABAAAE
1 11+AB3 ?Eúèè 111()+=+A B BABAê111()+=+A B AABB
29êAu1k
12101031
01010121
0021 00 23
0003 00 0 3
·?
12101031
01010121
0021 00 23
0003 00 0 3
+==
AEEC AACD
O B O D O BD
1231 23 52
0121 0 3 24
21 23 43
0303 09
+= +=
==
ACD
BD
1?
12101031 1252
0101 01 2 1 01 2 4
0021 00 2 3 00 4 3
00030003 0009
=
30ê"?-?L ,XEú-?L
? 1?
5200
2100
0083
0052
? 2?
1000
1200
2130
1214
·? (1)A?
5200
2100 52 83,,
0083 21 52
0052
= ==
AO AB
OB
1?
1
1
1
5200 1 200
2100 2500
0083 0023
0052 0 0 5 8
==
AO
OB
(2)A?
1000
1200 10 21 30,,,
2130 12 12 14
1214
= ===
AO ABC
BC
1
1
111
10 00
111000 00
221200
1112130 0
2631214
15 11
8 24 12 4
==
AO
CBAC
