线性代数
西南
大学
英文
课件
部分
m?1.0:?HO?5“m?S?:?:?K:)AK?f)K+3?:?i1L.uSK?i15L.2SKm?p?X?A?X:(?()?-:?2|$5),)K.)?;“?%K.5“m?:?gax=b(a 6=0).):ax=b a1a1ax=a1bx=a1b.?)?Ka.k.?e5lg,/?2.5“m?2/?n ggg:?ggg?O pppggg3,4g,k 5g,Galois=+,?=C-“n s 5|n 555|)?5m5C555“5“m?5|555|?/:n s a11x1+a12x2+a1nxn=b1a21x1+a22x2+a2nxn=b2as1x1+as2x2+asnxn=bs SSS.:3?,3?m.aij:1 i 1 j?X.:s=n;s n.|?):n?|(c1,c2,cn)?zC?.5“m?u5|?Ag,?K?k)?k?kk?O?ek)?ek),X)?ek),)m?Xo?t?AK,?5|?n.5“m?*N?ClA*ae:ax+by=c L?.d|?)eZ?:.uU?)?:;k;k.nC:ax+by+cz=d Lm?.d|?)meZ?:.uU?)?:;k;k.?,uy,5|?)kn.5“m?SNln?5|)?9?SN?%SN.kl?/u:s=n 1?(1)/:?n?(1?1n)l5|L?5m9?5C;?A?g.5“m?It is a cliche,but true nevertheless,that Mathematics canbe learned only by doing it,and not just by reading about it.While it is generally true that in order to learn Mathematicsone must do Mathematics,the serious student shouldattempt to solve a large number of problems.o1:1 30%,70%.5“m?eZP(Field)kvk)?k.X x+2=1(N,Z)2x=1(Z,Q)F?8,()U/?1,=T8?,()?(JE,38p.rVg(5:?P E8 C?f8.e P v 0,1 P;a,b P,a b,ab P?b 6=0,ab P.K P.5“m?eZP?O?k?O;u8,I?yv?=.Q,R,C;Z.?Q,R,C?,k?:Q(2)=a+b2|a,b Q,Q(i)=a+bi|a,b Q?y8.5“m?eZP5K?Q,?C.?e5?53,A?.5“m?eZP?P,/Xanxn+an1xn1+a1x+a0 P u x?,n N,an,an1,a1,a0 P.?f(x),g(x)L;e f(x)=anxn+an1xn1+a1x+a0 an6=0,K n f(x)?g.d f(x)n g.Px:L P k?8.Pnx L P kgL n?8.5“m?eZP?:?f(x)P,c P.e f(c)=0,K c f(x)?.-:e3 g(x)?f(x)=(x c)kg(x)g(c)6=0,K c f(x)?k-.“?nnn:nE C?n gk n(-U-O).5“m?eZPPnXi=1ai=a1+a2+an.nXj=1mXi=1aij=a11+a12+a1n+am1+amn=a11+a21+am1+a1n+amn=mXi=1nXj=1aij;?m=n,PnXi,j=1aij.5“m?eZPPmXj=1nXi=1aibi=nXi=1mXj=1aibj=(a1+a2+an)(b1+b2+bm);nYi=1ai=a1a2an.5“1?1.1:?n?1?HO?5“1?1?n?1?5|?,?5|?m?Xens=n;s n;s n.G?s=n,=?u?.?Ln?/.J?u?5|;.?f,L?)K?(a.k?u?5|?/:1 1 (?,vkd)2 2(?1)5“1?1?n?1?l?5|u(a11x1+a12x2=b1 (1)a21x1+a22x2=b2 (2)|:?x2:a22(1),a12(2)?(a11a22x1+a12a22x2=b1a22 (3)a12a21x1+a12a22x2=a12b2 (4)2?a11a22x1 a12a21x1=b1a22 a12b2?a11a22 a12a21=0,?|)k).?a11a22 a12a216=0,)?x1=b1a22 a12b2a11a22 a12a21;aq?x2=a11b2 b1a21a11a22 a12a215“1?1?n?1?o(?|(a11x1+a12x2=b1a21x1+a22x2=b2d?X(.?|k)?a11a22 a12a216=0.d)dex1=b1a22 a12b2a11a22 a12a21;x2=a11b2 b1a21a11a22 a12a21.K:BP.5“1?1?n?1?*?x1=b1a22 a12b2a11a22 a12a21;x2=a11b2 b1a21a11a22 a12a21.x1 x2?/;x1 x2?1;x1 x2?f1?/.PPPLLL:BuPL a11a22 a12a21,P?a11a12a21a22?.?111?:o1?La11a12a21a22 aij:i 1I,j?I.L a11a22 a12a21TL?111?.=?a11a12a21a22?=a11a22 a12a21.5“1?1?n?1?u?1?5)1683 cF?f?J.X?nuVandemonde(?).1?(Determinant),?i1 D det L1?:D=?a11a12a21a22?=a11a22 a12a21.51?A?P,LLLL.?1?K:?1?u?B?.5“1?1?n?1?1?L)1?PL x1=b1a22 a12b2a11a22 a12a21;x2=a11b2 b1a21a11a22 a12a21,?(a11x1+a12x2=b1a21x1+a22x2=b2?)x1=?b1a12b2a22?a11a12a21a22?,x2=?a11b1a21b2?a11a12a21a22?555:?XL?1?6=0,|k),)v)?1XL?1?.x1?fXL?1?O?AL?1?;x2?fXL?1?O?AL?1?.D LXL?1?,DiLXL1 i?O?AL?1?,Kxi=DiD,i=1,2.5“1?1?n?1?fzz,n?,?n?u i1?c1;i2m?u i2?c2;g?in1m?u in1?cn1;(i1i2in)=c1+c2+cn1.5“_SO(2341);(32514);(n(n 1)321);(36715284).(2341)=1+1+1=3;(32514)=2+1+2=5;(n(n 1)321)=(n 1)+(n 2)+2+1=n(n1)2;(36715248)=2+4+4+0+2+0+0=12.5“?5L?fuy?_S._S()?()?.(2341)=3?.(2143)=2?.*?2341 2143 m?X:1,3?iC.?i,j?C,?Cg.P(i,j).X 2341(1,3)2143.=?2341 Lg(1,3)C?2143.5“5nUC n?5.yyyy.(1)y?UC?5.?i j ()(i,j)j i ()?()(),Q i j?3?_;i j?3?_;d i,j|?:ij 3()/SK ji 3()/_S;ij 3()/_SK ji 3()/S.l?()=()1.=?UC?5.5“(2)y?UC?5.?ik1k2ksj ()(i,j)jk1k2ksi ()5?Le?y(i,k1),(i,k2),(i,ks),(i,j),(ks,j),(k2,j),(k1,j).?u?2s+1 g?.q?UC?5,UC?5.n?,n!2.5“