1、?Vg|?d3.2|HO?5“NSN1?Vg2|?d?Vg|?d?mmm:-a1,a2,a3 R,mL 2?kS|(a1,a2)a1a2!2?3?kS|(a1,a2,a3)a1a2a3 3?222(:R?P?:2 3?n?2?P?n?:5“?Vg|?dn?P?,P?n?kS|(a1,a2,an)a1a2.an(=(a1,a2,an)T)P?n?.aiT?1 i.?O,c1,?.PPP:?F1i1L n?,X,?.P k?n?8P Pn.X R29m R3.z 0?.5“?Vg|?dPn?$Pn?$:e =(a1,an),=(b1,bn),k P,:+=(a1+b1,an+bn);:k=(ka1
2、,kan).uve 8:(+)+=+(+);+=+;+0=;+()=0;1=;(+)=+;(+)=+;()=().5“?Vg|?dm(5m)Pn?9 8$K?“X P?n?m(5m).X:R2 2?mm R3 3?m5“?Vg|?d?|u?A=a11a12a1na21a22a2n.am1am2amn Pmn,g,/:A?z1 n?,r1 i (ai1,ai2,ain)Pi,K1,2,m A?1|.A?z?m?,r1 j a1ja2j.amjP j,K1,2,n A?|.5“?Vg|?dL5,e m n?1 1,2,m m n?A.e n m?1,2,n m n?A.l?A?1|?|;1|?|A
3、?;5“?Vg|?d5|a11x1+a12x2+a1nxn=b1a21x1+a22x2+a2nxn=b2am1x1+am2x2+amnxn=bmx1a11a21.am1+x2a12a22.am2+xna1na2n.amn=b1b2.bmq1q2qnqx11+x22+xnn=5“?Vg|?dl?5|L:x11+x22+xnn=/555|?/.w,1,2,n5|?X?A=a11a12a1na21a22a2nam1am2amn?|,d|?.?x11+xnn=,5“?Vg|?d5|5L|1,2,s9 k1,k2,ks P,k11+k22+kss|1,2,s?5|.k1,k2,ks|X.?Pn,e3 c
4、1,c2,cs P,?=c11+c22+css,K d|1,2,s5L.5“?Vg|?d#Vg5|:5|x11+x22+xnn=k)m|c1,c2,cn P s.t.c11+c22+cnn=m d 1,2,n5L(:|k)?UdX?|5L5“?Vg|?d555|/?(VVV):J?5|k)?#?-lA?w5|;|5|Ud 1,2,nL,S5|x11+x22+xnn=k)=.5“?Vg|?df?1=111,2=110,3=100,=345.y d|1,2,35L.yyydu=51 2 3.d|1,2,35L.ed|L?O:5“?Vg|?dd|L?O d 1,2,n5Lm5|x11+x22+xnn
5、=k)m5|?X?uO2?mr(1,2,n)=r(1,2,n,)m?d 1,2,n9 1,2,n,?5“?Vg|?df?1=1122,2=1213,3=1140,=1031.y d|1,2,35L,L.)?(1,2,3,)?1?1C(1,2,3,)=1111121021432301r2r1 r32r1,r42r11111012101210121r3+r2,r4r2 r1r210320121000000005“?Vg|?dfu r(1,2,3)=r(1,2,3,).?d 1,2,35L.5|x11+x22+x33=(1.1)5L?|X.d?(1,2,3,)?1C?(J,?5|(1.1)?|(x1
6、=3x3+2x2=2x3 1?)=,X-x3=0,?)x1=2,x2=1,x3=0.uk=21 2+03=21 2+03.555L?:X-x3=1.5“?Vg|?d5fm d 1,2,s5Lm U?1,2,s?5|ggg:1,2,sk?5|,2?.1,2,sk?5|?8:W=k11+k22+kss|k1,k2,ks P W v:=k11+kss,=11+ss W,+=(k1+1)1+(ks+s)s W;P,=(k1)1+(ks)s W.W u4.5“?Vg|?d5fm?6=U Pn,e U v(1),U=+U;(2)U,P=U,K U Pn?5fm,fm.0 Pn:fm.U=(a,b,0)|a
7、,b R R3?fm.W fm,d 1,sk5|?,d 1,s)?fm,Ph1,si?yyy888fffmmm:n:(1);(2)4;(3)4.5“NSN1?Vg2|?d?Vg|?d|?d?!,?Ud 1,s5L?K.!?X?|m?LK.?1,s(2.1)1,t(2.2)Pn?|.e|(2.1)?zd(2.2)L,K|(2.1)d|(2.2)L.e(2.1)(2.2)UpL,K(2.1)(2.2)?d,P1,s 1,t.555|?d?dX:ggg,DDD444.5“?Vg|?df?1=111,2=110,3=100,4=123,1=100,2=010,3=001.y|1,2,3,4|1,2,3
8、?d.yyy1=1+2+3,2=1+2,3=1,4=1+22+33 1,2,3,4d 1,2,3L.q1=32=2 3,3=1 2,u 1,2,3d 1,2,3,4L.?1,2,3,4|1,2,3?d.5“?Vg|?d?|?d/e,|?|1,s 1,t?d:?g?id 1,tL,i=1,s;g?jd 1,sL,j=1,t.n s+t 5|)?.O?.?5?Ud|L:d 1,sL r(1,s)=r(1,s,).u|5?|m?pL,?|?d.5“?Vg|?d?|?d?y 1,s 1,t:,I?y 1,td 1,sLr(1,s)=r(1,s,1,t);1,sd 1,tLr(1,t)=r(1,t,1,
9、s).n5 1,s 1,tr(1,s)=r(1,s,1,t)qr(1,t)=r(1,t,1,s)5“?Vg|?d?|?dn1,s 1,tr(1,s)=r(1,s,1,t)=r(1,t)yyy ky75.d 1,s 1,t 1,td1,sL.AO/,1d 1,sL,ur(1,s)=r(1,s,1);q 2d 1,sL,?,2d 1,s,1L,ur(1,s,1)=r(1,s,1,2);-EL,B?r(1,s)=r(1,s,1,t)5“?Vg|?d?|?d2d 1,s 1,t 1,sd 1,tL.nyr(1,t)=r(1,t,1,s).?A=(1,s,1,t)B=(1,t,1,s),A L?CC B
10、,?CUC?,l?r(1,s,1,t)=r(1,t,1,s).n?r(1,s)=r(1,s,1,t)=r(1,t)5“?Vg|?d?|?d2y5.?r(1,s)=r(1,s,1,t)=r(1,t).u?1 j t,d?r(1,s)r(1,s,j)r(1,s,1,t)u r(1,s)=r(1,s,j),=jd 1,s5L.l?1,sd 1,t5L.u?1 i s,?r(1,t)r(1,t,i)r(1,s,1,t)u r(1,t)=r(1,t,i),=id 1,t5L.l?1,td 1,s5L.5“?Vg|?df?1=1111,2=3113,1=2011,2=1102,3=3120.y|1,2|1
11、,2,3?d.yyy?(1,2,1,2,3)?1C(1,2,1,2,3)=13213110111110213120r4+r1 r2+r1,r3r15“?Vg|?df13213042220211106333r3+12r2 r432r213213042220000000000r(1,2)=r(1,2,3)=r(1,2,1,2,3).|1,2|1,2,3?d.5“3.355HO?5“3!,5|kvk)8(?UdX?|5L=AX=B x11+x22+xnn=.e5NUUd|5L?K.klN?fm.5|x1+2x2=32x1+3x2=44x1 5x2=6(0.1)5|(0.1)?/x1124+x2235
12、=3465“-1=124,2=235,=346 5|(0.1)?/?x11+x22=.w,1,2,m.?1,2?.5“-1=124,2=235,=346 5|(0.1)?/?x11+x22=.w,1,2,m.?1,2?.5“-1=124,2=235,=346 5|(0.1)?/?x11+x22=.w,1,2,m.?1,2?.5“|m)XA?:?x1,x2?H,x11+x22Ld 1,2(?1.x11+x22=k)3 1.,d 1,2,n?.3f,uy555LLLA?k?X.e,?m 1,2?,3d 1,25L 1,2,3?;4Ud 1,25L 1,2,4?;,u?,ke51,2,3?0?k1,
13、k2,k3 P,s.t.k11+k22+k33=01,2,4?e 11+22+44=0,K 1=2=4=0.5“55?f?u:Ud|5L,La.?|5.?*?(a2?m,m?#?Vg:555,m?,#?Vg:555:?1,s Pn,s 1.e3?k1,k2,ks P?k11+k22+kss=0K|1,s5.K5.=ek11+k22+kss=0=k1=k2=ks=0K|1,s5.5“55?5)d,|o5,o5.A5|?55.555555555“?(.w,?n5,?n5;?5,?5.55?,?2.Am?n)m?55.5“55?f?|5?.01+0i1+1 0+0i+1+0s=0.?55:5 k 6
14、=0 s.t.k=0 =0.5 6=0.?1=10.0,2=01.0,n=00.1,K 1,2,n5.5“e k11+k22+knn=0,Kk1k2.kn=0,l?k1=k2=kn=0.=1,2,n5.?1=111,2=025,3=247,?1,2,3?5.du21 2+3=0.1,2,35.5“?1,2,35 1=1+2,2=2+3,3=3+1.K 1,2,35.e k11+k22+k33=0,Kk1(1+2)+k2(2+3)+k3(3+1)=0.l?(k1+k3)1+(k1+k2)2+(k2+k3)3=0.du 1,2,35,l?k1+k3=0k1+k2=0k2+k3=0 k1=k2=k3
15、=0,?y.5“X?|?5|1,2,s5mg5|x11+x22+xss=0 k)n1,2,s5 r(1,2,s)=s.yyy1,2,s5mx11+x22+xss=0 k)mX?u?,=r(1,2,s)=s5“?1,2,s Pn,e s n,K 1,2,s5.AO/,n+1 n?75.yyy w,(1,2,s)n 1 s?,?r(1,2,s)mins,n=n s.l?1,2,s5.5“|?E|?|?1,2,s Pn,i1 i2 it s.i1,i2,it1,2,s?|.?|5=|5|5=?|5|?|?1=a11.an1,s=a1s.ans,t 1:5“01=a11.an1a(n+1)1.a(n+t)1,0s=a1s.ansa(n+1)s.a(n+t)s|1,s?|.e,?7L?3.?3?t ,?I?yz?.?|5=?|5?|5=?|55“yyy?|5=?|5e 1,s5,Kg5|x11+xss=0(0.2)k).w,(0.2)g5|x101+xs0s=0(0.3)?c n|?|.u(0.3)?)(0.2)?).d(0.3)k).=01,0s5.5“
