隊(duì)列式練習(xí)題及隊(duì)列式練習(xí)題及隊(duì)列式練習(xí)題及線性代數(shù)作業(yè)學(xué)號(hào)__________________姓名________________第1章隊(duì)列式(作業(yè)1)一、填空題1．設(shè)自然數(shù)從小到大為標(biāo)準(zhǔn)次序，則擺列13(2n1)24(2n)的逆序數(shù)為，擺列13(2n1)(2n)(2n2)2的逆序數(shù)為.2．在6階隊(duì)列式中，a23a42a31a56a14a65這項(xiàng)的符號(hào)為.3．全部n元擺列中，奇擺列的個(gè)數(shù)共個(gè).二、選擇題00010002001.由定義計(jì)算隊(duì)列式=（）.n100000000nn(n1)(n1)(n2)（A）n!（B）(1)2n!（C）(1)2n!（D）(1)n(n1)n!xx102．在函數(shù)f(x)1x23中，x3的系數(shù)是（）.23x2112xA）1（B）-1（C）2（D）33．四階隊(duì)列式的睜開式中含有因子a32的項(xiàng)，共有（）個(gè).（A）4；（B）2；（C）6；（D）8.三、請(qǐng)按以下不一樣要求正確寫出n階隊(duì)列式Ddet(aij)定義式：1．各項(xiàng)以行標(biāo)為標(biāo)準(zhǔn)次序擺列；2．各項(xiàng)以列標(biāo)為標(biāo)準(zhǔn)次序擺列；3．各項(xiàng)隊(duì)列標(biāo)均以任意次序擺列.四、若n階隊(duì)列式中，等于零的元素個(gè)數(shù)大于n2n，則此隊(duì)列式的值等于多少？說(shuō)明原由.06.2版第1章第1頁(yè)共11頁(yè)線性代數(shù)作業(yè)學(xué)號(hào)__________________姓名________________第1章隊(duì)列式(作業(yè)2)一、填空題a11a12a134a112a113a12a131．若D=a21a22a231,則D14a212a213a22a23_____.a31a32a334a312a313a32a33112312x223的根為___________.2．方程31=0252319x2二、計(jì)算題2134a1001．419162．1b103015456001c111718001dabbbab3．Dnbba06.2版第1章第2頁(yè)共11頁(yè)線性代數(shù)作業(yè)學(xué)號(hào)__________________姓名________________xa1a2an11a1xa2an11a1a2xan114.Dn1a1a2a3x1a1a2a3an1x11x12x1nx21x22x2n5．計(jì)算n階隊(duì)列式Dn(n2)。xn1xn2xnn06.2版第1章第3頁(yè)共11頁(yè)線性代數(shù)作業(yè)學(xué)號(hào)__________________姓名________________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,則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（）.111111111aa2a31000（A）abcd；（B）0bacada；（C）1bb2b3；（D）1babb2a2b2c2d20bcd1cc2c31cacc2a4b4c4d40b3c3d31dd2d31dadd2三、計(jì)算題15131．設(shè)A1134A42A43A44,（j，，，）A中元素a4j的代11232234數(shù)余子式.06.2版第1章第4頁(yè)共11頁(yè)線性代數(shù)作業(yè)學(xué)號(hào)__________________姓名________________x10000x1002．000x1anan1an2a2xa1an(a1)n(an)nan1(a1)n1(an)n13．Dn1aa1an111anbn04．D2na1b100d1c10cndn06.2版第1章第5頁(yè)共11頁(yè)線性代數(shù)作業(yè)學(xué)號(hào)__________________姓名________________第1章隊(duì)列式(作業(yè)4)一、填空題a1x1a2x2a3x3d11．已知關(guān)于變量xi(i1,3)的線性方程組b1x1b2x2b3x3d2，由克萊姆法規(guī)，當(dāng)滿足c1x1c2x2c3x3d3條件時(shí)，方程組有獨(dú)一解，且x3.a11xaxan1x

1a12x2a1nxn01a22x2a2nxn0D，那么D0是該隊(duì)列式有的系數(shù)隊(duì)列式為1an2x2annxn0非零解的條件.二、求解下排隊(duì)列式0123n11012n21．Dn2101n33210n4n1n2n3n4006.2版第1章第6頁(yè)共11頁(yè)線性代數(shù)作業(yè)學(xué)號(hào)__________________姓名________________1a11111a21,此中a1a2an0.2．Dn111an(1)x12x24x30三、問(wèn)取何值時(shí)，齊次線性方程組2x1(3)x2x30有非零解？x1x2(1)x3006.2版第1章第7頁(yè)共11頁(yè)線性代數(shù)作業(yè)學(xué)號(hào)__________________姓名________________第1章隊(duì)列式(檢測(cè)題)一、填空題1．若擺列i1i2in的逆序數(shù)為k，則擺列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)1a1a2x2an11a1a2an1

,此中a1,a2,,an1是互不同樣得實(shí)xn1數(shù)，則方程P（x）=0（）。（A）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)角線翻轉(zhuǎn)，挨次得an1anna1nannanna1nD1，D2，D3，則（）a11a1na11an1an1a11nn(n1)（A）D1D2D3D；（B）；D1(1)2D,D2( )2D,D3Dn(n1)n(n1)（C）D1D2D,D3(1)2D；（D）D1D2(1)2D,D3D。06.2版第1章第8頁(yè)共11頁(yè)線性代數(shù)作業(yè)學(xué)號(hào)__________________姓名________________三、計(jì)算題32140aba13512．a(chǎn)0ab。1．222；1023ba0a5412aba01231819202121718193211617183．D；191817212201918321a1xxxxa2xx4．Dn(aix,i1,n)xxan1xxxxan06.2版第1章第9頁(yè)共11頁(yè)線性代數(shù)作業(yè)學(xué)號(hào)__________________姓名________________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)a1pa2p2anpn；2.(1)t(qiq2qn)aq1aq2aqn.112n(pip2pn)(qiq2qn)3．(1)t(pip2pn)t(q1q2qn)apqapq2apqn.四.值為0.112n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；2.abcdabcdad1；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1.0.2.xn(1)n1yn.二、選擇題1(B).2（C），（D）06.2版第1章第10頁(yè)共11頁(yè)線性代數(shù)作業(yè)學(xué)號(hào)__________________姓名________________三、計(jì)算題1.6；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1.b1b2b30，c1c2c3a1a2a3b1b2b3c1c2c3nn1)。2.aj(1三、當(dāng)0,2或3時(shí)，該齊次線性方程組確有非零解.