南航大线性代数作业答案2.pdf

《南航大线性代数作业答案2.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、3.求以下行列式的值.122222221222222222220222(1)D22nnn1222120212222nnn22202222222222232201002(n2)!22nn120030222nn0002(2)(3)教材例题.axaa112naaxa122n(4)D,其中xi0,1,2,,.niaaax12nnnaxain12ai1axaa112nnaax12

2、2aniaxax222an解：D=i1aaax12nnnaxain2axnni11aaxaa21nn2n1axaxaxa22nn222aii11aaxxaax22nnnnn1aaxaa21nn2n00xxxx02212aii100xxx0xnn1nnnnnxxi1axxii1axiiii12ii22xinnx1xxaii

3、11ai2i2xinnaixi1i1i2xi第三节ababbabaan1b1.(1)Dab1babaabbannn1ab1ababab(2)D2nbababaab000bab0ab21nabba1abbaba000aba02221nn211aD22nnb11D22n12222abD22nabD2abn2222又因为D22ab,Dabnba11

4、11aa12aan2222(3)Daa12aannnnnaa12aannn1xxij1!1nn1!11!11jinnn(1)nn!1!1!12n1nn(1)ni!12i0123nnnn1232n(4)D21nnnn222332(1nnnn)1(1)2(1nn)3n123nnnnn2222nnnn0,当n3.2(1n

5、nnn)1(1)2(1nn)3n12当时nD22,;34当时nD11,.x1x1x1(5)Dkx1aaaaxakk12k21解：按第一列展开：kk11DxDa(1)(1)xDakk11kkk2xxDkkkkkk21aaxD21xaakk23xDxaxaa23kk1kkkixaixk,2i1x12其中Dxxaa.212axa2121xx2xxx12(6)Dxx1x2

6、x1x22Dx(1)DxD,nn12n22(n3)DDxDD()(xDD),nn11nn23221xx22322其中Dxxx1(1xxx)2(1),32xx121xx222Dx(1)x,22xx12nDDx,nn122nn22nDDxDxxnn12n22nn26xxxD2n2kxn.(2)k02.证明略.第四节1.(1)例题.xyz1,(2)axbycza,abc,,互不相同.2bcx

7、cayabza,111解：Dabcbacacb()()()0,bccaab故由Cramer法则存在唯一解，则111aabc(2)Dabca()bcbca(2),x,1()caba()2acaab11122bcaDaacac()()abc,y,2()cbba()2bcaab11122abcDababaab()()c,z.3()cacb()2bccaaxxxax0,1234xxxa20x,12342.xxxx30,1

8、234xxaxbx0,1234解：当系数行列式D0.时，只有全零解111aa111121aa010041D11310041aaba111ab00aba12(1ab)4()a2(1ab)40.第五节1.(1)无解.(2)xxxx12348,3,6,0.(3