一道行列式的多种计算法

©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:(1979-),,,(,710121):,,n:;;;;:O151.22:A:1007-3264(2009)03-0133-02,,,,:Dn=1+a111111+a211111+a311111+an,ai0(i=1,2,,n):():DnRi-R1i=2,3,,n1+a1111-a1a200-a10a30-a100anC1+a1aiCii=2,3,,n1+a1+ni=2a1ai1110a20000a30000an=(a2a3an)1+a1+ni=2a1ai=(a2a3an)1+ni=1a1ai():Dn=(a1a2an)1+1a11a21a31an1a11+1a21a31an1a11a21+1a31an1a11a21a31+1anCi+ni=2Ci(a1a2an)1+ni=11ai11a21a31an11+1a21a31an11a21+1a31an11a21a31+1anRi-R1i=2,3,,n(a1a2an)1+ni=11ai11a21a31an010000100001©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=(a1a2an)1+ni=11ai():Dn=1111101+a1111011+a2110111+a3101111+anRi-R1i=2,3,,n+111111-1a1000-10a200-100a30-1000anCi+n+1i=2Ci1+ni=11ai11110a100000a200000a300000an=(a1a2an)1+ni=11ai():Dn=1+a111111+a211111+a310001+1+a111011+a210111+a30111an=a10010a201001+a310001+anDn-1=a1a2an-1+an(a1a2an-2+an-1Dn-2)=a1a2an-1+a1a2an-2an+an-1anDn-2=a1a2an+1+a1a2an-2an+a1a2an-3an-1an+an-2an-1anDn-3==a1a2an-1+a1a2an-2an+a1a2an-3an-1an+a1a3an-1an+a2a3an-1an=(a1a2an)1+ni=11ai()Dncj-cj+1j=1,2,,n-1a100001-a2a200010-a3a300100-a4001000-an-1an-110000-an-11+an-1=cn(1+an-1)a10000-a2a20000-a3a300000an-20000-an-1an-1n-1+(-1)(n-1)+na10000-a2a20000-a3a300000an-200000-ann-1+(-1)(n-2)+na10000-a2a20000-a3a30000000-an-1an-10000-ann-1++(-1)1+n-a2a20000-a3a30000-a40000000-an-1an-10000-ann-1=(1+an)a1a2an-1+a1a2an-3an-2an++a2a3an=(1+ni=11ai)ni=1ai,:,,,,(146)43120095©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[2].TCP/IP[J].,2006,(2):113-115.[3],.[J].,2005,(8):19-21.[4],.VOD[J].,2003,(01):23-25.[5].:[J].,2005,(2):64-65.[6].[J].,2007,(09):87.ComparativestudyofmultimediasurportingplatforminremoteeducationMAXian-yan(SchoolofAdultEducation,XianUniversityofPostandTelecommunications,Xian710121,China)Abstract:Startingwiththedefinition,architecture,andprotocolsofmultimediacommunication,thispaperde2scribestheapplicationofmultimediacommunicationsysteminremoteeducation.Therearetwobasicsolutionsformultimediacommunicationinremoteeducations:oneisvideoconferencesolution,anotherisnetworkbasedsolution.Thispaperprovidesdetailcomparisonofthetwosolutionsabove.Keywords:distanteducation;multimediacommunicationsystem;network;GEM(134)[1].[M].:,2005.[2].[M].:,2007.VarietyofnumerationmethodsofadeterminantZHANGHu-dong(DepartmentofAppliedMathematicsandPhysics,XianUniversityofPostandTelecommunications,Xian710121,China)Abstract:SincethenumerationofdeterminantisanimportantanddifficultcomposingportionofthecourseofLinearAlgebra,thispapergivesvarietyofnumerationmethodsofadeterminant,andsumsupmajornumera2tionmethodsofthenumeration.Keywords:arrowheadeddeterminant;borderedmethod;dismantleditemmethod;recursivemethod;order-re2ductionmethod64120095