行列式練習題目及答案

1、第一章行列式一、單項選擇題000100101=().(A)001001000001001002.,=().(A)000011000(B)-1(C)1(D)2(B)-1(C)1(D)2aaa2aaa-2a1112131111311123.若D=aaa1，則D=2aaa-2a=(2122232121232122aaa2aaa-2a31323331333132(A)4(B)-4(C)2(D)-2若aa則aka41112=a，1222=().aaaka21221121(A)ka(B)-ka(C)k2a(D)-k2a5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

2、,則x=().(A)0(B)-3(C)3(D)2-87436-2316.若D=:1，11則D中第仃兀的代數(shù)余子式的和為（)4375(A)-1(B)2(C)3(D)030407.若D=01-100，則D中第四行兀的余子式的和為（）.53-22(A)-1(B)2(C)3(D)0x+x+kx=0123&k等于下列選項中哪個值時，齊次線性方程組h+kx+x=0有非零解.123kx+x+x=01231110()(A)-1(B)-2(C)-3(D)0二、填空題1.行列式o101110010010000202.行列式000n一1n000a113.行列式"21aa1(n-1)1na02(n-

3、1)aa11a12a13a11a13-3a123a124.如果D=aaa=M,則D=aa-3a3a212223121232222aaaaa-3a3a31323331333232n1005.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1-11X一1,1-1x+1一16.行列式x-11-1x+1-11一11+九1111+九-17.n階行列式11-1+九有元素，則所得的新行列式的值為8.已知三階行列式中第二列元素依次為1,2,3,其對應的余子式依次為3,2,1則該行列式的值為.123££r9.設行列式D=,小c43248,A(j二1,2,3,4)為D中第四行

4、元的代數(shù)余子式,14j51一311設行列式D=11A+A=4142,A+A=4344則4A+3A4142+2A42+A44abca10已知D=cbab,D中第四列兀的代數(shù)余子式的和為baccacbd2 343 44=-6,A為a(j=1,2,3,4)的代數(shù)余子式，則5674j4j1221352n-1120012已知行列式D=1030,D中第行兀的代數(shù)余子式的和為100nkx+2x+x=012313齊次線性方程組px+kx=0僅有零解的充要條件是12x-x+x=012314.若齊次線性方程組2x+5x=0有非零解，則k=232-3x-2x123+kx=03三、計算題abcdxyx+ya2b2c2

5、d21.2yx+yxa3b3c3d3x+yxyb+c+da+c+da+b+da+b+c01x1101xx110=0;1x104.二1.0;2.(1)n1n!;n(n1)3.(1)2aaa1n2(n1)n14.-3M;5.一160;6.x4;a01111a11111a12111an(a.豐1,j=0丄,n)；j1111111131b11baaa1111112b16.bbaa；1222111(n-1)-bbbba123nxaaa12n1+x2xxxxaxaa1121n12n8.xx1+x2xxaaxa;2122n；12nxxxx-1+x2aaaxn1n2n123210001-aa000121001aa000120010.D=011aa00011aa0002100011a000125.79.參考答案單項選擇題CDCCA填空題7.(九+n)九n1；8.-2;9.0;10.0;11.12,-9;12.n!(l-Y1)；13.kH-2,3;k=114.k=7三計算題1.(a+b+c+d)(ba)(ca)(da)(cb)(db)(dc)；2.2(x3+y3)；3.x=-2,0,1;4.I!(a-1)(1+工-)；ka1k=0k=0