行列式練習(xí)題

隊(duì)列式學(xué)習(xí)復(fù)習(xí)計(jì)劃練習(xí)題及答案隊(duì)列式學(xué)習(xí)復(fù)習(xí)計(jì)劃練習(xí)題及答案PAGEPAGE13隊(duì)列式學(xué)習(xí)復(fù)習(xí)計(jì)劃練習(xí)題及答案PAGE第1章隊(duì)列式(作業(yè)1)一、填空1．自然數(shù)從小到大準(zhǔn)序次，擺列13?(2n1)24?(2n)的逆序數(shù)，擺列13?(2n1)(2n)(2n2)?2的逆序數(shù).2．在6隊(duì)列式中，a23a42a31a56a14a65的符號(hào).3．全部n元擺列中，奇擺列的個(gè)數(shù)共個(gè).二、0001000200=〔〕.n100000000nn(n1)(n1)(n2)n(n1)〔A〕n!〔B〕(1)2!〔C〕(1)2n!〔D〕(1)n!nxx102．在函數(shù)f(x)1x23中，x3的系數(shù)是〔〕.23x2112x〔A〕1〔B〕-1〔C〕2〔D〕33．四隊(duì)列式的睜開(kāi)式中含有因子a32的，共有〔〕個(gè).〔A〕4；〔B〕2；〔C〕6；〔D〕8.三、按以下不一樣要求正確寫(xiě)出n隊(duì)列式Ddet(aij)定式：1．各以行準(zhǔn)序擺列；2．各以列準(zhǔn)序擺列；3．各隊(duì)列均以隨意序擺列.四、假定n隊(duì)列式中，等于零的元素個(gè)數(shù)大于n2n，此隊(duì)列式的等于多少？明原因.第1章隊(duì)列式(作業(yè)2)一、填空題a11a12a134a112a113a12a131．假定D=a21a22a231,那么D14a212a213a22a23_____.a31a32a334a312a313a32a3311232．方程12x223的根為_(kāi)__________.231=052319x2二、計(jì)算題2134a1001．419162．1b103015456001c111718001dabbbab3．Dnbbaxa1a2an11a1xa2an114.a1a2xan11Dn1a1a2a3x1a1a2a3an1x11x12x1nx21x22x2n2)。5．計(jì)算n階隊(duì)列式Dn(nxn1xn2xnn第1章隊(duì)列式(作業(yè)3)一、填空題0a12a13a1na120a23a2n1．當(dāng)n為奇數(shù)時(shí)，隊(duì)列式a13a230a3n=_________.a1na2na3n0xy0000xy002．隊(duì)列式.000xyy000x二、選擇題1．設(shè)D是n階隊(duì)列式,那么以下各式中正確的選項(xiàng)是().[Aij是D中aij的代數(shù)余子式].nn(A)aijAij0,j1,2,,n;(B)aijAijD,j1,2,,n;i1i1nn(C)a1jA2jD;(D)aijAij0,i1,2,,n.j1j12．隊(duì)列式結(jié)果等于(ba)(ca)(da)(cb)(db)(dc)的隊(duì)列式是〔〕.1111〔A〕abcda2b2c2d2a4b4c4d4三、計(jì)算題

11111aa2a31000；〔B〕0bacada；〔C〕1bb2b3；〔D〕1babb20bcd1cc2c31cacc20b3c3d31dd2d31dadd215131．設(shè)1134A〔j1，2，3，4〕是A中元素a4j的代A，計(jì)算A41A42A43A44,此中12132234數(shù)余子式.x10000x1002．000x1anan1an2a2xa1an(a1)n(an)nan1(a1)n1(an)n13．Dn1aa1an111anbn04．D2na1b100c1d10cndn第1章隊(duì)列式(作業(yè)4)一、填空題a1x1a2x2a3x3d11．對(duì)于變量xi(i1,3)的線(xiàn)性方程組b1x1b2x2b3x3d2，由克萊姆法那么，當(dāng)知足c1x1c2x2c3x3d3條件時(shí)，方程組有獨(dú)一解，且x3.a11x1a12x2a1nxn02．齊次線(xiàn)性方程組a21x1a22x2a2nxn0D，那么D0是該隊(duì)列式有的系數(shù)隊(duì)列式為an1x1an2x2annxn0非零解的條件.二、求解以下隊(duì)列式0123n11012n22101n31．Dn210n43n1n2n3n401a11111a21此中a1a2an0.2．Dn,111an(1)x12x24x30三、問(wèn)取何值時(shí)，齊次線(xiàn)性方程組2x1(3)x2x30有非零解？x1x2(1)x30第1章隊(duì)列式(檢測(cè)題)一、填空題1．假定擺列i1i2in的逆序數(shù)為k，那么擺列inin1i1的逆序數(shù)為.a1a2000a3a40002．Dc1c2231.c3c4014c5c6450a1na2nan1nanna1n1a2n2an1n103．n階隊(duì)列式=.a12a2200a110001222234．1111=.144243155253二、選擇題1a1a2an11a1x1a2an11．設(shè)P(x)1a1a2x2an1,此中a1,a2,,an1是互不同樣得實(shí)1a1a2an1xn1數(shù)，那么方程P〔x〕=0〔〕?！睞〕無(wú)實(shí)根；〔B〕根為1，2，。。。，n-1；〔C〕根為-1，-2，。。。，-〔n-1〕；〔D〕根為0。2．設(shè)n階隊(duì)列式Ddet(aij),把D上下翻轉(zhuǎn)、或逆時(shí)針旋轉(zhuǎn)90、或依副對(duì)角線(xiàn)翻轉(zhuǎn)，挨次得an1anna1nannanna1nD1，D2，D3，那么〔〕a11a1na11an1an1a11nn(n1)〔A〕D1D2D3D；〔B〕；D1(1)2D,D2()2D,D3Dn(n1)n(n1)〔C〕D1D2D,D3(1)2D；〔D〕D1D2(1)2D,D3D。三、計(jì)算題32141351222；1．102354121231819202121718193．D321161718；191817212201918321

0aba2．a(chǎn)0ab。ba0aaba0a1xxxxa2xx4．Dn(aix,i1,n)xxan1xxxxan四、證明題1．隊(duì)列式D中的每個(gè)數(shù)aij分別用bij(b0)去乘，試證所得隊(duì)列式D1與D相等.2cos100012cos1002．證明012cos00sin(n1)Dnsin0002cos100012cos答案第1章隊(duì)列式(作業(yè)1)答案一.填空題1．n(n1)，n(n1).2．正號(hào).3．n!22二、選擇題1．〔C〕；2．〔B〕；3．〔C〕三、1．(1)t(pip2pn)a1p1a2p2anpn；2.(1)t(qiq2qn)aq11aq22aqnn.(pip2pn)(qiq2qn)3．(1)t(pip2pn)t(q1q2qn)ap1q1ap2q2apnqn.四.值為0.第1章隊(duì)列式(作業(yè)2)答案一、填空題1．-12。2?！?,±2.n二、計(jì)算題1．0；abcdad1；3.[a(n1)b](ab)n1；4.(xai)；i15．當(dāng)n=2時(shí)，D2x1x2；當(dāng)n>2時(shí),用拆項(xiàng)法可得Dn0。第1章隊(duì)列式(作業(yè)3)答案一、填空題n(1)n1yn.二、選擇題1(B).2〔C〕，〔D〕三、計(jì)算題；2．xna1xn1nan1xan；3.(ij)；4.D2n(aidibici).n1ij1i1第1章隊(duì)列式(作業(yè)4)答案a1a2d1a1a2a3b1b2d2c1c2d3。2.充要條件.二、1．(1)n1(n1)2n2；一、填空題1b2b30，c1c2c3a1a2a3b1b2b3c1c2c3nn1)。三、當(dāng)2.aj(10,2或3時(shí)，該齊次線(xiàn)性方程組確有非零解.j1j1aj第1章隊(duì)列式(檢測(cè)題