资源描述:
《线性代数习题集(带答案).pdf》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库。
1、第一部分专项同步练习第一章行列式一、单项选择题1.下列排列是5阶偶排列的是().(A)24315(B)14325(C)41523(D)243512.如果n阶排列j1j2jn的逆序数是k,则排列jnj2j1的逆序数是().n!n(n1)(A)k(B)nk(C)k(D)k223.n阶行列式的展开式中含a11a12的项共有()项.(A)0(B)n2(C)(n2)!(D)(n1)!000100104.().01001000(A)0(B)1(C)1(D)2001001005.().00011000(A)0(B)1(C)1(D)22xx111x1236.在函数f(x)中x项的系数是().32x300
2、01(A)0(B)1(C)1(D)21/99a11a12a132a11a13a112a1217.若Da21a22a23,则D12a21a23a212a22().2a31a32a332a31a33a312a32(A)4(B)4(C)2(D)2a11a12a12ka228.若a,则().a21a22a11ka2122(A)ka(B)ka(C)ka(D)ka9.已知4阶行列式中第1行元依次是4,0,1,3,第3行元的余子式依次为2,5,1,x,则x().(A)0(B)3(C)3(D)28743623110.若D,则D中第一行元的代数余子式的和为().11114375(A)1(B)2(C)3(D
3、)03040111111.若D,则D中第四行元的余子式的和为().01005322(A)1(B)2(C)3(D)0x1x2kx3012.k等于下列选项中哪个值时,齐次线性方程组x1kx2x30有非零解.kx1x2x30()(A)1(B)2(C)3(D)0二、填空题1.2n阶排列24(2n)13(2n1)的逆序数是.2.在六阶行列式中项a32a54a41a65a13a26所带的符号是.3.四阶行列式中包含a22a43且带正号的项是.24.若一个n阶行列式中至少有nn1个元素等于0,则这个行列式的值等于.111001015.行列式.01110010010000206.行列式.000n1n00
4、0a11a1(n1)a1na21a2(n1)07.行列式.an100a11a12a13a11a133a123a128.如果Da21a22a23M,则D1a21a233a223a22.a31a32a33a31a333a323a329.已知某5阶行列式的值为5,将其第一行与第5行交换并转置,再用2乘所有元素,则所得的新行列式的值为.3/99111x111x1110.行列式.1x111x111111111111.n阶行列式.11112.已知三阶行列式中第二列元素依次为1,2,3,其对应的余子式依次为3,2,1,则该行列式的值为.1234567813.设行列式D,A4j(j1,2,3,4)为D中
5、第四行元的代数余子式,43218765则4A413A422A43A44.abcacbab14.已知D,D中第四列元的代数余子式的和为.baccacbd1234334415.设行列式D6,A4j为a4j(j1,2,3,4)的代数余子式,则15671122A41A42,A43A44.1352n1120016.已知行列式D1030,D中第一行元的代数余子式的和为100n.kx12x2x3017.齐次线性方程组2x1kx20仅有零解的充要条件是.x1x2x30x12x2x3018.若齐次线性方程组2x25x30有非零解,则k=.3x12x2kx30三、计算题abcdxyxy2222abcd1.3
6、333;2.yxyx;abcdxyxybcdacdabdabcxa1a2an2101x1a1xa2an21101xa1a2xan213.解方程0;4.;x1101x10a1a2a3x1a1a2a3an115/99a01111a1115.11a21(aj1,j0,1,,n);111an111131b116.112b1111(n1)b1111xa1a2anb1a1a1a1a1xa2an7.b1b2a2a2;8.a1a2xan;b1b2b3ana1a2a3x2100021x1x1x2x1xn121002x2x11x2x2xn012009.;10.2xnx1xnx21xn00021000121a
7、a00011aa0011.D011aa0.0011aa00011a四、证明题211aa12aa211bb12bb1.设abcd1,证明:0.211c2c1cc211d2d1dda1b1xa1xb1c1a1b1c122.a2b2xa2xb2c2(1x)a2b2c2.a3b3xa3xb3c3a3b3c31111abcd3.(ba)(ca)(da)(cb)(db)(dc)(abcd).2222abcd4444abcd111a1a2an22