大学线性代数行列式答案

1、第一章行列式一、利用对角线法则计算下列行列式2.2.,=sin8+cos8=12.1. =1(-1)(-5)21(-3)322-3(-1)(-3)-211-(-5)22=5-612-9-220=20-141021021.解：x31031-2x=-18-x+2x2=04x20x-6解得x范德蒙德x=2x=3x=1x=2x=3解：(341782659)=2+2+3+3+1=11解："987654321)=8+7+6+5+4+3+2+1=36解：E(n1)H|321)=(n2)+|)|+2+1=12)213l|l(2n-1)2n(2n-2)|1|2解：(13|(2n1)2n(2n一2川|2

2、)=24.(2n一2)=n(n一1)四、计算行列式2.解:3012302030454500200100012000122030L01=62=12020020000010010030000030000400041.解:=2134=24214-1124-1124-13-12-1-132-1056-2123-2213-20-3-50506-2056-2056-23.解:2. =0(b-a)(b-a)(b-a)12431111111111112314231401-1201-12=10=10=10413241320-3-1-200-44342134210112000Y5.解:=1606解:-abacae

3、-bce-111111bd-cdde=adfb-ce=abcdef1-11=abcdef0-20=4abcdefbfcf-efbc-e11-100-27.解:xaIIIax+(n-1)ax+(n-1)aHIx+(n-1)a11川1aHIaax|Haax"Ia*R1=x+(n1)appq，q，1rpi-+FFF*F1>aa川xaaHIxaa巾x0=x+(n_1)a+x-a山=(xa)nx(n1)a11山0。川x-a9.解:416525=(5-4)(5-3)(5-1)(4-3)(4-1)(3-1)=124132=48xy0III00xy0IH00y00HI000xyIII000xy

4、IH00xy0HI00IHIIIIIIIIIIIIHl=xIHHIinIHmIII+(-1广yIIIHIIIIHIHIm000IIIxy000IHxy000HIy0：y00III0x000IH0x(nJ.)000HIxy8.解:(n=)nyn二x(-1)n127641251x001x001x001x00-11-xy001y001y001y00-11-yz0-11-yz001z001z00-11-z00-11-z00-11-z000110.解:=111.解:210III000121III000川IIIIIIHI川III000III121000III01212.解:1+110III000110HI

5、0001100001+021III000121HI000021山000InIIIIIIIIIII*IHIIIIIIIII10川HIIII+IIIIIIIHII*inIH000III121000HI121000III121000III012000HI012000III012110III000210HI000011III000121HI000IIIIIIIIIIIIHIn*+IIIIIIIIIIHHIIII二14Tn_1000III011000HI121000III001000HI012n-41 In4=1In2.,12-1I11=218238232331000800203111115495494

6、991000500409a8569=2乂10“=2妇06166766767710006006071234198698686610009008063976111111111111=2x1060123=2乂1060123=2601小10623032-100-4-1000-4-10064306-8-150605110-30106-21133In=n1此题有I可题不做此题太难，感兴趣的同学下课后参考我练习册五、解答题ai3a22a34a4ia55,-35a22a34a4ia53解：由丁e(431265)=6，所以a23a31a42a56a14a65正号T(452316)=6,所Ha32a43ai4a5

7、ia66a25正号k2+k一一解：=k26k-4#0Mk#3士JT32k-4-1解：含有x3的项只能是aaqqx3,即系数为略（此题不做）解：=0解：此题唯一解求不出2舄-I方程组有唯一解则K-iI#0,55-Ii-55-52"2=(%1)(5"4)#0-62. 4即,1,5解：舄11111P11-岛1012卜11一舄2卜-101-,1-'-121只有当丸=1或者卜=0时有非零解3a113a123a13a1a12a13解：-2a212a22-2a23=3K（-2）K（-1）a21a22a23-a31a32a33a31a32a33=615=901012解：23=-=3

8、4511.解：D-一162（-2）0（一8）（1）1-一641-一1112111III1120川0A1+A12+Il|+An=103III0+ddbt+44F-I100IIIn1311+100IIIn/1=n!（1一）i=2n13此题太难，感兴趣的同学课后参考我联系册六、用克莱姆法则求解方程组1.解1-D=112 1-砌1347则X1=，x2=,x3=055则xi10,X2434解：D=3=-28-15=-43,D1043=10,D2=-733.11105110151021-1111-1121-11D=18,D1=17,D2=35,12-1122-1112-1110233023132311501115211121-11D3=38,D4=13122112-1210331023解:血17353813Xi=,X2,X3,X4=-一181818184.略七、证明题1.aXbyaybzazbXayazaXaz+bXaX+byay+bzyaz+bXyyaz+bXxyaz+bxzaX+by+abzzaX+by=ayzax+byxay+bzxxay+bzzxay+bzX2=ayzyzXyXXyzzX+a2byzy3=ayzXXyzXzzXyX3=ayz证明:丁是根据行列式的定义，Dn的展开式中的每一项至少含有一个因子为0,所以该行列式为零八、应用题解：设抛物线的方程为y=ax?+b