1、工程數(shù)學(xué)（線性代數(shù)與概率統(tǒng)計(jì)）習(xí)題一211. 221(1)5;1 2X1122322. 22(X1)(XX1)XXX1；XXX1ab,2213. _ab2a2ba2b21114. 314532278153658950a05. b0c0,（第一行與第三行對(duì)應(yīng)成比例）0d01236. 312182766618o231二.求逆序數(shù)1. 34215即5221002. 4312即532003.n(n1)(n1)(n2)21即(n1)(n2)1021n(n1)213014.(2n1)(2n)(2n2)n1n1n212(n1)(n1)(n2)212*n(n1)2四階行列式中含有a1a23的項(xiàng)為ana23a3

2、2a44a1a23a34a42四.計(jì)算行列式值2.41240724009451202r14r21202r17r412021052010r2015220B15r400178501170117011701.0110111113.111004abcdef5.b2b2ca2b2cab2aa2c2aa2c2a2b(ab1)(cd1)ad2a2b2aa2c2a2b2aa2c2a2b4.按第一行展開(kāi)其中a2a2a2bbac2b2c2ccaba2a2a2bb2b2c2cc122abc212221a2a2bb2c2ca2a02bb02c2ca(ab)2b2ab25abc3ab(ab)(ac)(a其余同法可求。方

3、法2:abc2a2a2bbac2b2c2ccabbac2b(abc)2ccab6.224131202a2bcaba2a02bb02c2cb(aa02a2ba2b2c0cabc)2c2acaba2a(ac)2ccabab3ac)2b2b2a2ccab40r22rl223530323r32r10451卜4n0240558311a02a2bc2b2c0cab2bbac2a2c2c27012221000222222227. 2232r2(i2)10010222n|000n28.a00a001000a010按第一行展開(kāi)a00aa00002(n2)!0a000010nn1nn2na(1)(1)aa五.證明

4、下列等式2a2ab22cd2(a(b(c(daba1221)1)1)(b(c(d2)2)2)a122a(b2)2)2)2)a(bb(a(b(c(d3)3)3)3)a)(a(b(c(db22(b1a)(ab)33)3)3)3)2-，,一一a2a14a46a9a22a12b22b14b46b9"2c2b22b12c22c14c46c9c42c2c22c122d22d14d46d9d22d123333c4Gc3c13.anan2an3a2同理Dk1XDkak,返回代入得DnXDn1anX(XDn2an1)XDnan(1)n11(1)n2XDn1anann1a1X1XanX1000X1000

5、0X1000X10000X00按第一行展開(kāi)X00X00000X1000X1anan1an2a2xa1an1an2an3a2X1000Dn六、計(jì)算下列各式31.設(shè)X1,x2,x3為萬(wàn)程xPXq0的二個(gè)根,則由三次方程根的性質(zhì)3.2axbxCXX1X2X3b/a,X1X2X3x1x2x2x3x1x3c/a得x3pxq0的三個(gè)根滿足：Xix2x30,XiX2X3qx1X2x3所以x3x1x2x13x3x33x1x2x3p(x1x2x3)3q3x1x2x30。X2x3x12.f(x)3.求D3中x3的系數(shù)為-1.A14A24A34的A14A24A34A44的值,4.求D的AmAn2Ann的值，A1入2

6、riarn(ia0000xa0000xa01111xn)(xa)n1七.計(jì)算行列式值1.nx1mx2xn為mx2xni1nx1x2mxnnDnc1cjj2x1x2xnmXmx2mxni1nXmx2xnmi1XimX2i1riri(i2,n)0mxnn0(xim)(m)n1i12.123110Dn022000n1n0000各行提出公因子11(n1)!0021103010n1n00001CjCj1(jn1,1)nkk10(n1)!八nkk210nkk3012n1n0000000013.n(n1)!(1)n1kk1(1)n1(n1)!2D2n按第一行展開(kāi)b(1)2n12n12n1adD2n2bcD2n2,同理D2n(adbc)D2n4,D2ad所以D2n(adbc)n4.a1a1Dnrir1(i2,n)a1a2a211a20a2ana1八.克萊姆法則解方程2y1.2x2z解:1210211011202118D11114D22114D3211112312132113D12即x1/2,y1/2,z3/2；Xi2.Xi2x23x34x44x2x3x433x2x417x23x3解:44234116,D131111130113731x43123011D130073128D210104