1、L (6 )5 IsEmail: qv d9,q430072Wuhan University“ cBc T1=c # 17 c MLZF33 c_ FLM148cM #=Q69Bc T5 -%.cyp A/5: 5.(2), (5); 7; 8.(2). (+5|y ) .) ?CzE, h (.1 . LE59 / T:(1)flflflflflflflfl2 0 11 4 11 8 3flflflflflflflfl; (2)flflflflflflflfla b cb c ac a bflflflflflflflfl;(3)flflflflflflflfl1 1 1a b ca2 b2
2、c2flflflflflflflfl; (4)flflflflflflflflx y x+yy x+y xx+y x yflflflflflflflfl.: (1)flflflflflflflfl2 0 11 4 11 8 3flflflflflflflfl= 2(4)3+0(1)(1)+1180132(1)81(4)(1)= 24+8+164= 4:(2) flflflflflflflfla b cb c ac a bflflflflflflflfl= acb+bac+cbabbbaaaccc = 3abca3 b3 c3:(3) flflflflflflflfl1 1 1a b ca2 b
3、2 c2flflflflflflflfl= bc2 +ca2 +ab2 ac2 ba2 cb2 = (ab)(bc)(ca):(4) flflflflflflflflx y x+yy x+y xx+y x yflflflflflflflfl= x(x+y)y +yx(x+y)+(x+y)yxy3 (x+y)3 x3= 3xy(x+y)y3 3x2y 3y2xx3 y3 x3= 2(x3 +y3):2 .1 VlvSQ, p/ I :(1) 1 2 3 4; (2) 4 1 3 2;(3) 3 4 2 1; (4) 2 4 1 3;(5) 1 3(2n1) 2 4(2n);(6) 1 3(2n1
4、) (2n) (2n2)2.(1) I 0.(2) I 4: 4 1, 4 3, 4 2, 3 2.12Bc T(3) I 5: 3 2, 3 1, 4 2, 4 1, 2 1.(4) I 3: 2 1, 4 1, 4 3.(5) I n(n1)2 :3 2.15 2, 5 4 . 27 2, 7 4, 7 63(2n1) 2, (2n1) 4, (2n1) 6, ., (2n1) (2n2)(n1)(6) I n(n1):3 2.15 2, 5 4 . 27 2, 7 4, 7 63(2n1) 2, (2n1) 4, (2n1) 6, ., (2n1) (2n2)(n1)4 2.16 2,
5、6 4 2(2n) 2, (2n) 4, (2n) 6, ., (2n) (2n2) .(n1)3 . Tcy0a11a23.:l, TB(1)ta1p1a2p2a3p3a4p4;tp1p2p3p4 I p1 = 1, p2 = 3X%, p1p2p3p4 ? 13,13241342. I tsY0+0+1+0 = 1;0+0+0+2 = 2:, a11a23a32a44a11a23a34a42 p.4 .9 / T:(1)flflflflflflflflflfl4 1 2 41 2 0 210 5 2 00 1 1 7flflflflflflflflflfl; (2)flflflflflfl
6、flflflfl2 1 4 13 1 2 11 2 3 25 0 6 2flflflflflflflflflfl;(3)flflflflflflflflab ac aebd cd debf cf efflflflflflflflfl; (4)flflflflflflflflflfla 1 0 01 b 1 00 1 c 10 0 1 dflflflflflflflflflfl.: (1) flflflflflflflflflfl4 1 2 41 2 0 210 5 2 00 1 1 7flflflflflflflflflflr1$r2= flflflflflflflflflfl1 2 0 24
7、 1 2 410 5 2 00 1 1 7flflflflflflflflflflr24r1=r310r1 flflflflflflflflflfl1 2 0 20 7 2 40 15 2 200 1 1 7flflflflflflflflflflL (6 )5 Is3r2$r4=flflflflflflflflflfl1 2 0 20 1 1 70 15 2 200 7 2 4flflflflflflflflflflr4+7r2=r3+15r2flflflflflflflflflfl1 2 0 20 1 1 70 0 17 850 0 9 45flflflflflflflflflfl= 17
8、9flflflflflflflflflfl1 2 0 20 1 1 70 0 1 50 0 1 5flflflflflflflflflfl= 0:(2) flflflflflflflflflfl2 1 4 13 1 2 11 2 3 25 0 6 2flflflflflflflflflflc4c2=flflflflflflflflflfl2 1 4 03 1 2 21 2 3 05 0 6 2flflflflflflflflflflr4r2=flflflflflflflflflfl2 1 4 03 1 2 21 2 3 02 1 4 0flflflflflflflflflflr4r1=flfl
9、flflflflflflflfl2 1 4 03 1 2 21 2 3 00 0 0 0flflflflflflflflflfl= 0:(3) flflflflflflflflab ac aebd cd debf cf efflflflflflflflfl= adfflflflflflflflflb c eb c eb c eflflflflflflflfl= adfbceflflflflflflflfl1 1 11 1 11 1 1flflflflflflflflr2+r1=r3+r1 adfbceflflflflflflflfl1 1 10 0 20 2 0flflflflflflflfl
10、= adfbceflflflflfl0 22 0flflflflfl = 4abcdef:(4) flflflflflflflflflfla 1 0 01 b 1 00 1 c 10 0 1 dflflflflflflflflflflr1+ar2=flflflflflflflflflfl0 1+ab a 01 b 1 00 1 c 10 0 1 dflflflflflflflflflfl1 =Z 7(1)(1)2+1flflflflflflflfl1+ab a 01 c 10 1 dflflflflflflflflc3+dc2=flflflflflflflfl1+ab a ad1 c 1+cd
11、0 1 0flflflflflflflfl3=Z 7(1)(1)3+2flflflflfl1+ab ad1 1+cdflflflflfl = abcd+ab+cd+ad+1:5 . :(1)flflflflflflflfla2 ab b22a a+b 2b1 1 1flflflflflflflfl= (ab)3; flflflflflflflfla2 ab b22a a+b 2b1 1 1flflflflflflflflc2c1=c3c1flflflflflflflfla2 aba2 b2 a22a ba 2b2a1 0 0flflflflflflflfl=(1)3+1flflflflflab
12、a2 b2 a2ba 2b2aflflflflfl = (ba)(ba)flflflflfla b+a1 2flflflflfl = (ab)3:(2)flflflflflflflflax+by ay +bz az +bxay +bz az +bx ax+byaz +bx ax+by ay +bzflflflflflflflfl= (a3 +b3)flflflflflflflflx y zy z xz x yflflflflflflflfl;4Bc T :flflflflflflflflax+by ay +bz az +bxay +bz az +bx ax+byaz +bx ax+by ay
13、+bzflflflflflflflfl1 =s 7aflflflflflflflflx ay +bz az +bxy az +bx ax+byz ax+by ay +bzflflflflflflflfl+bflflflflflflflfly ay +bz az +bxz az +bx ax+byx ax+by ay +bzflflflflflflflflQ= 7a2flflflflflflflflx ay +bz zy az +bx xz ax+by yflflflflflflflfl+0+0+b2flflflflflflflfly z az +bxz x ax+byx y ay +bzflf
14、lflflflflflflQ= 7a3flflflflflflflflx y zy z xz x yflflflflflflflfl+b3flflflflflflflfly z xz x yx y zflflflflflflflfl=a3flflflflflflflflx y zy z xz x yflflflflflflflfl+b3(1)2flflflflflflflflx y zy z xz x yflflflflflflflfl= (a3 +b3)flflflflflflflflx y zy z xz x yflflflflflflflfl:N5B“E:flflflflflflflfl
15、ax+by ay +bz az +bxay +bz az +bx ax+byaz +bx ax+by ay +bzflflflflflflflfl=flflflflflflflflax ay azay az axaz ax ayflflflflflflflfl+flflflflflflflflby bz bxbz bx bybx by bzflflflflflflflfl=a3flflflflflflflflx y zy z xz x yflflflflflflflfl+b3flflflflflflflfly z xz x yx y zflflflflflflflfl= a3flflflflf
16、lflflflx y zy z xz x yflflflflflflflfl+b3(1)2flflflflflflflflx y zy z xz x yflflflflflflflfl=(a3 +b3)flflflflflflflflx y zy z xz x yflflflflflflflfl:E A “, L5 Bp! ij1xi xj= (1)n(n+1)2Yn+1ij1(ai+1)(aj +1)= (1)n(n+1)2Yn+1ij1(ij)= (1)n(n+1)2 (1)n+(n1)+1 Yn+1ij1(ij)=Yn+1ij1(ij):(4) D2n =flflflflflflflfl
17、flflflflflflflflflan 0 bn. .0 a1 b1c1 d10. .cn 0 dnflflflflflflflflflflflflflflflflfl;:ZEB.|c2nT2n1Q M #,M= ;|r2nT2n1QM #,M12Bc T=:D2n = (1)2n1(1)2n1flflflflflflflflflflflflflflflflflflflflflflan bncn dnan1 bn1. .a1 b1c1 d1. .cn1 dn1flflflflflflflflflflflflflflflflflflflflflfl= (andn bncn)D2(n1);n =
18、 1 HD2 =flflflflfla1 b1c1 d1flflflflfl = a1d1 b1c1, D2n = (andn bncn)(a1d1 b1c1) =nYi=1(aidi bici):ZEP.15 11M.5(1)l59 NZE.ZE=.D2nZ 7r1= anflflflflflflflflflflflflflflflflflflflan1 0 bn1 0. .0 a1 b1c1 d10 . .cn1 0 dn1 00 0 dnflflflflflflflflflflflflflflflflflflfl+(1)2n+1bnflflflflflflflflflflflflflfl
19、flflflflfl0 an1 0 bn1. .0 . a1 b1c1 d10. .0 cn1 dn1cn 0 0 0flflflflflflflflflflflflflflflflflflflZ 7c2n1= andnD2n2 bncnD2n2:Nw T:D2n = (andn bncn)D2n2;D2n =nYi=2(aidi bici)D2.7D2 =flflflflfla1 b1c1 d1flflflflfl = a1d1 b1c1,D2n =nYi=1(aidi bici).(5) Dn = det(aij), aij = jijj;:aij = jijjDn = det(aij)
20、=flflflflflflflflflflflflflflflfl0 1 2 3 n11 0 1 2 n22 1 0 1 n3. . . . .n2 n3 n4 n5 1n1 n2 n3 n4 0flflflflflflflflflflflflflflflflL (6 )5 Is13riri+1=i=1;2;flflflflflflflflflflflflflflflfl1 1 1 1 11 1 1 1 11 1 1 1 1. . . . .1 1 1 1 1n1 n2 n3 n4 0flflflflflflflflflflflflflflflflcj+c1=j=2;3;flflflflflf
21、lflflflflflflflflflfl1 0 0 0 01 2 0 0 01 2 2 0 0. . . . .1 2 2 2 0n1 2n3 2n4 2n5 n1flflflflflflflflflflflflflflflfl=(1)n1(n1)2n2:(6) Dn =flflflflflflflflflflfl1+a1 1 11 1+a2 1. . .1 1 1+anflflflflflflflflflflfl, a1a2an 6= 0.: 6E.Dn =flflflflflflflflflflflflfl1 1 1 10 1+a1 1 10 1 1+a2 1. . . .0 1 1 1
22、+anflflflflflflflflflflflflfl(n+1)(n+1)rir1=i=2;3;flflflflflflflflflflflflfl1 1 1 11 a1 0 01 0 a2 0. . . .1 0 0 anflflflflflflflflflflflflfl(n+1)(n+1)c1+ 1a1c2=flflflflflflflflflflflflfl1+ 1a1 1 1 10 a1 0 01 0 a2 0. . . .1 0 0 anflflflflflflflflflflflflfl(n+1)(n+1)c1+ 1aj cj+1=j=2;3;flflflflflflflfl
23、flflflflfl1+ 1a1 + 1a2 + 1an 1 1 10 a1 0 00 0 a2 0. . . .0 0 0 anflflflflflflflflflflflflfl(n+1)(n+1)=(a1a2an)1+nXi=11ai:14Bc T8 . X E5/ ZF:(1)8:x1 +x2 +x3 +x4 = 5;x1 +2x2 x3 +4x4 = 2;2x1 3x2 x3 5x4 = 2;3x1 +x2 +2x3 +11x4 = 0;:D =flflflflflflflflflfl1 1 1 11 2 1 42 3 1 53 1 2 11flflflflflflflflflfl=
24、flflflflflflflflflfl1 1 1 10 1 2 30 5 3 70 2 1 8flflflflflflflflflfl=flflflflflflflflflfl1 1 1 10 1 2 30 0 13 80 0 5 14flflflflflflflflflfl=flflflflflflflflflfl1 1 1 10 1 2 30 0 1 540 0 0 142flflflflflflflflflfl= 142:D1 =flflflflflflflflflfl5 1 1 12 2 1 42 3 1 50 1 2 11flflflflflflflflflfl=flflflflf
25、lflflflflfl5 1 1 100 5 5 182 3 5 280 1 0 0flflflflflflflflflfl=flflflflflflflfl5 1 100 5 182 5 28flflflflflflflfl=flflflflflflflfl5 1 104 0 1023 0 22flflflflflflflfl= 142;D2 =flflflflflflflflflfl1 5 1 11 2 1 42 2 1 53 0 2 11flflflflflflflflflfl=flflflflflflflflflfl1 5 1 10 7 2 30 12 3 70 15 1 8flflf
26、lflflflflflflfl=flflflflflflflflflfl1 5 1 10 1 3 20 0 23 110 0 39 31flflflflflflflflflfl=flflflflflflflflflfl1 5 1 10 1 3 20 0 1 190 0 0 284flflflflflflflflflfl= 284;D3 =flflflflflflflflflfl1 1 5 11 2 2 42 3 2 53 1 0 11flflflflflflflflflfl= 426; D4 =flflflflflflflflflfl1 1 1 51 2 1 22 3 1 23 1 2 0fl
27、flflflflflflflflfl= 142:,x1 = D1D = 1 ; x2 = D2D = 2 ; x3 = D3D = 3 ; x4 = D4D = 1:(2)8:5x1+6x2 = 1;x1+5x2+6x3 = 0;x2+5x3+6x4 = 0;x3+5x4+6x5= 0;x4+5x5= 1:“ TD55 =flflflflflflflflflflflflfl5 61 5 61 5 61 5 61 5flflflflflflflflflflflflflZ 7c1= 5D44 flflflflflflflflflfl6 0 0 01 5 6 00 1 5 60 0 1 5flflf
28、lflflflflflflfl= 5D44 6flflflflflflflfl5 6 01 5 60 1 5flflflflflflflfl= 5D44 6D33:B TD55 = 5D44 6D33,D33 = 5D22 6D11 = 5(256)65 = 65;D44 = 5D33 6D22 = 565619 = 211;L (6 )5 Is15D55 = 5D44 6D33 = 5211665 = 665:D1 =flflflflflflflflflflflflfl1 6 0 0 00 5 6 0 00 1 5 6 00 0 1 5 61 0 0 1 5flflflflflflflflf
29、lflflflflZ 7c1= D44 +flflflflflflflflflfl6 0 0 05 6 0 01 5 6 00 1 5 6flflflflflflflflflfl= D44 +64 = 211+64 = 1507:D2 =flflflflflflflflflflflflfl5 1 0 0 01 0 6 0 00 0 5 6 00 0 1 5 60 1 0 1 5flflflflflflflflflflflflflZ 7c2=flflflflflflflflflfl1 6 0 00 5 6 00 1 5 60 0 1 5flflflflflflflflflfl+(1)5+2flf
30、lflflflflflflflfl5 0 0 01 6 0 00 5 6 00 1 5 6flflflflflflflflflflZ 7c2= D33 563 = 651080 = 1145:D3 =flflflflflflflflflflflflfl5 6 1 0 01 5 0 0 00 1 0 6 00 0 0 5 60 0 1 1 5flflflflflflflflflflflflflZ 7c3= (1)1+3flflflflflflflflflfl1 5 0 00 1 6 00 0 5 60 0 1 5flflflflflflflflflfl+(1)5+3flflflflflflflf
31、lflfl5 6 0 01 5 0 00 1 6 00 0 5 6flflflflflflflflflflZ 7c2= D22 66D22 = 703:D4 =flflflflflflflflflflflflfl5 6 0 1 01 5 6 0 00 1 5 0 00 0 1 0 60 0 0 1 5flflflflflflflflflflflflflZ 7c4= (1)1+4flflflflflflflflflfl1 5 6 00 1 5 00 0 1 60 0 0 5flflflflflflflflflfl+(1)5+4flflflflflflflflflfl5 6 0 01 5 6 00
32、 1 5 00 0 1 6flflflflflflflflflflZ 7c4= 56D33 = 5665 = 395:D5 =flflflflflflflflflflflflfl5 6 0 0 11 5 6 0 00 1 5 6 00 0 1 5 00 0 0 1 1flflflflflflflflflflflflflZ 7c5= (1)1+5flflflflflflflflflfl1 5 6 00 1 5 60 0 1 50 0 0 1flflflflflflflflflfl+flflflflflflflflflfl5 6 0 01 5 6 00 1 5 60 0 1 5flflflflfl
33、flflflflfl= 1+D44 = 1+211 = 212:,x1 = 1507665 ; x2 = 1145665 ; x3 = 703665; x4 = 395665; x5 = 212665:9 ., | H, QLZF8:x1 +x2 +x3 = 0;x1 +x2 +x3 = 0;x1 +2x2 +x3 = 0:d ,?16Bc T:“ D =flflflflflflflfl 1 11 11 2 1flflflflflflflflr3r1=flflflflflflflfl 1 11 10 0flflflflflflflfl= (1)3+2flflflflfl 11 1flflflf
34、lfl = (1):1 P QLZFd ,5D = 0,(1) = 0; = 0 = 1.10 . | H, QLZF8:(1)x1 2x2 +4x3= 0;2x1+(3)x2 +x3= 0;x1 +x2+(1)x3= 0:d ,?:“ D =flflflflflflflfl1 2 42 3 11 1 1flflflflflflflflc2c1=flflflflflflflfl1 3+ 42 1 11 0 1flflflflflflflfl= 1(1)3+1flflflflfl3+ 41 1flflflflfl+(1)(1)3+3flflflflfl1 3+2 1flflflflfl= (3)
35、4(1)+(1)3 2(1)(3+)= (1)3 +2(1)2 +3= (2)(3):QLZFd ,5D = 0,(2)(3) = 0: = 0, = 2 = 3.=c # 1 .XLM: 8:x1 = 2y1 +2y2 +y3;x2 = 3y1 +y2 +5y3;x3 = 3y1 +2y2 +3y3;pVM x1;x2;x3M y1;y2;y3LM.:ZEB.hEZ,y1, y2, y3. .ZE=. Z.X:0BBx1x2x31CCA =0BB2 2 13 1 53 2 31CCA0BBy1y2y21CCA;#0BBy1y2y21CCA =0BB2 2 13 1 53 2 31CCA10B
36、Bx1x2x31CCA =0BB7 4 96 3 73 2 41CCA0BBy1y2y31CCA:8:y1 = 7x1 4x2 +9x3;y2 = 6x1 +3x2 7x3;y3 = 3x1 +2x2 4x3:ZE . X E5Z.“ D =flflflflflflflfl2 2 13 1 53 2 3flflflflflflflflc12c3=c22c3flflflflflflflfl0 0 17 9 53 4 3flflflflflflflfl= 1:,y1 = 1Dflflflflflflflflx1 2 1x2 1 5x3 2 3flflflflflflflfl= x1flflflfl
37、fl1 52 3flflflflflx2flflflflfl2 12 3flflflflfl+x3flflflflfl2 11 5flflflflfl = 7x1 4x2 +9x3 ; y2 = 6x1 +3x2 7x3, y3 = 3x1 +2x2 4x3.2 .X LM8:x1 = 2y1 +y3;x2 = 2y1 +3y2 +2y3;x3 = 4y1 +y2 +5y3;8:y1 = 3z1 +z2;y2 = 2z1 +z3;y3 = z2 +3z3;pVz1, z2, z3x1, x2, x3LM.:ZEB. .1 :x1 = 2y1 +y3= 2(3z1 +z2)+(z2 +3z3)=
38、 6z1 +z2 +3z3:1718=c # ZEe, V ? Pc M.ZE=.X0BBx1x2x31CCA =0BB2 0 12 3 24 1 51CCA0BBy1y2y21CCA;0BBy1y2y21CCA =0BB3 1 02 0 10 1 31CCA0BBz1z2z31CCA:,0BBx1x2x31CCA =0BB2 0 12 3 24 1 51CCA0BBy1y2y21CCA =0BB2 0 12 3 24 1 51CCA0BB3 1 02 0 10 1 31CCA0BBz1z2z31CCA=0BB6 1 312 4 910 1 161CCA0BBz1z2z31CCA:8:x1 =
39、 6z1 +z2 +3z3;x2 = 12z1 4z2 +9z3;x3 = 10z1 z2 +16z3:3 . !A =0BB1 1 11 1 11 1 11CCA, B =0BB1 2 31 2 40 5 11CCA;p3AB2A#ATB:3AB2A = 30BB1 1 11 1 11 1 11CCA0BB1 2 31 2 40 5 11CCA20BB1 1 11 1 11 1 11CCA= 30BB0 5 80 5 62 9 01CCA20BB1 1 11 1 11 1 11CCA =0BB2 13 222 17 204 29 21CCA:ATB =0BB1 1 11 1 11 1 11C
40、CA0BB1 2 31 2 40 5 11CCA =0BB0 5 80 5 62 9 01CCA:4 .9 / :(1)0BB4 3 11 2 35 7 01CCA0BB7211CCA; (2) (1; 2; 3)0BB3211CCA;(3)0BB2131CCA(1; 2);L (6 )5 Is19(4)2 1 4 01 1 3 4!0BBBB1 3 10 1 21 3 14 0 21CCCCA;(5) (x1;x2;x3)0BBa11 a12 a13a12 a22 a23a13 a23 a331CCA0BBx1x2x31CCA;(6)0BBBB1 2 1 00 1 0 10 0 2 10 0
41、 0 31CCCCA0BBBB1 0 3 10 1 2 10 0 2 30 0 0 31CCCCA.: (1)0BB4 3 11 2 35 7 01CCA0BB7211CCA =0BB47+32+1117+(2)2+3157+72+011CCA =0BB356491CCA:(2) (1; 2; 3)0BB3211CCA = (13+22+31) = (10) = 10:(3)0BB2131CCA(1; 2) =0BB2(1) 221(1) 123(1) 321CCA =0BB2 41 23 61CCA:(4)2 1 4 01 1 3 4!0BBBB1 3 10 1 21 3 14 0 21CC
42、CCA=6 7 820 5 6!.(5)(x1; x2; x3)0BBa11 a12 a13a12 a22 a23a13 a23 a331CCA0BBx1x2x31CCA=(a11x1 +a12x2 +a13x3; a12x1 +a22x2 +a23x3; a13x1 +a23x2 +a33x3)0BBx1x2x31CCA=a11x21 +a22x22 +a33x23 +2a12x1x2 +2a13x1x3 +2a23x2x3:(6)0BBBB1 2 1 00 1 0 10 0 2 10 0 0 31CCCCA0BBBB1 0 3 10 1 2 10 0 2 30 0 0 31CCCCA=0BBBB1 2 5 20 1 2 40 0 4 30 0 0 91CCCCA.5 . !A =1 21 3!, B =1 01 2!,:(1) AB = BA ?(2) (A+B)2 = A2 +2AB +B2 ?(3) (A+B)(AB) = A2 B2 ?: (1)yAB =3 44 6!; BA =1 23 8!;20=c # ,AB 6= BA:(2)y(A+B)2 =2
