線性代數(shù)習(xí)題(帶答案解析)1262

第一部分專項同步練習(xí)第一章行列式一、單項選擇題1．下列排列是5階偶排列的是().(A)24315(B)14325(C)41523(D)243512．如果n階排列jj的逆序數(shù)是k,則排列jjjj的逆序數(shù)是().12nn21(D)n(n1)2(A)k(B)nk(C)n!2kk3.n階行列式的展開式中含aa的項共有()項.1112(A)0(B)n2(C)(n2)!(D)(n1)!00014．0010(0100).1000(A)0(B)1(C)1(D)200100100(00015.).1000(A)0(B)1(C)1(D)22xx11f(x)312x1x32中x3項的系數(shù)是().6．在函數(shù)0001(A)0(B)1(C)1(D)2aa11a2aaa2a1112a1，則D2aaa2a().121311137.若Daaa221223223121232122a31a332a31aa2a333132(A)4(B)4(C)2).(D)2aa12a，則a12ka22(8．若11aaaka11212122(A)ka(B)ka(C)k2a(D)k2a9．已知4階行列式中第1行元依次是4,0,1,3,第3行元的余子式依次為2,5,1,x,則x().(A)0(B)3(C)3(D)287436231，則D中第一行元的代數(shù)余子式的和為().10.若D11114375(A)1(B)2(C)3(D)03040D10111010，則D中第四行元的余子式的和為().11.若5322(A)1(B)2(C)3(D)0xxkx012.k等于下列選項中哪個值時，齊次線性方程組xkxx0有非零解.123123kxxx0123()(A)1(B)2(C)3(D)0二、填空題1.2n階排列24(2n)13(2n1)的逆序數(shù)是.2．在六階行列式中項3．四階行列式中包含aaaaaa所帶的符號是325441651326.aa且?guī)д柕捻検?243.4．若一個n階行列式中至少有n2n1個元素等于0,則這個行列式的值等于.11105.行列式01010111.0010010002006．行列式.000n1n000aaa1n111(n1)aa07．行列式.212(n1)a00n1aa11aaM，則Daa3a3a23aa3a3a1212131113128．如果Daa.21aa22121232222aa3a3a31333232a3331329．已知某5階行列式的值為5，將其第一行與第5行交換并轉(zhuǎn)置，再用2乘所有元素，則所得的新行列式的值為.111x111x111x111x111110．行列式.11111111．n階行列式.11112．已知三階行列式中第二列元素依次為1,2,3,其對應(yīng)的余子式依次為3,2,1，則該行列式的值為.12345678，A(j1,2,3,4)為D中第四行元的代數(shù)余子式，13．設(shè)行列式D43214j8765則4A3A2AA.41424344abcaDcbab，D中第四列元的代數(shù)余子式的和為bacc.14．已知acbd1234D33446，A15．設(shè)行列式AA為a(j1,2,3,4)的代數(shù)余子式，則4j15674j1122，AA.414243441351202n10016．已知行列式D103，D中第一行元的代數(shù)余子式的和為100n.kx2xx017．齊次線性方程組2xkx1230僅有零解的充要條件是.12xxx0123x2xx018．若齊次線性方程組有非零解，則=k.1232x5x0233x2xkx0123三、計算題abcdxyxya2b2c2d21.;2．；yxyxa3b3c3d3xyxybcdacdabdabcxaa1axaaaa1122n2n2n201x113．解方程101x0；x1104．a(chǎn)ax1；121x10aaax112aaa3a1123n1a1101a1111a111(a1,5.6.7.j0,1,,n)；2j111an11111131b1112b111(n1)b1111xaa1axa128．a(chǎn)axa2nbaaa1a2aa1bba11；nn;12212bbb1aaaa1x23n2321012101210.0000001xxx12xx1nxx2n21xx1x9.;2212xxxxn1n21x20002112n0001aa00000011aa11．.D11aa0000011aa011a四、證明題