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1、计算n阶行列式的若干方法举例（Examplesofsomemethodsforcalculatingorderndeterminant）Forexample,somemethodsforcalculatingnorderdeterminantLANminAbstract:"linearalgebra"isascienceandengineeringuniversitystudentsacompulsorymathematicscurriculum.Thecalculationofdeterminantisdifficultinlinearalgebra,especiallyt
2、hecalculationoftheNdeterminant,thestudentsinthelearningprocess,generallytherearemanydifficulties,difficulttograsp.TherearemanymethodsforcalculatingtheNdeterminant,butspecifictoasinglequestion,accordingtoitscharacteristics,selecttheappropriatemethod.Keywords:thecalculationmethodofnorderdeter
3、minantAlotofcalculationmethodofNdeterminant,unlessthezeroelementscanbeusedtocalculate(lessdefinedinacolumnorarowSTARTIIfullexpansion),moreistheuseofthepropertiesofthedeterminantcalculation,withparticularattentiontoobservethecharacteristicsfortheproblem,themethodisflexible,itisworthnoting.On
4、edeterminant,sometimesadifferentmethod.Herearesomecommonlyusedmethods,andexamples.1.usingthedirectcalculationofdeterminant1casesofdeterminantEMBEDEquation.DSMT4TheDnsolutionisnotzerowithgeneralformisexpressedasEMBEDEquation.DSMT4.TheinversenumberTcolumnarrangement(n-1N-2...1n)isequaltoEMBED
5、Equation.DSMT4,soEMBEDEquation.DSMT42.usingthepropertiesofthedeterminantcalculation2casesofaEMBEDEquation.DSMT4norderdeterminantelementsmeetEMBEDEquation.DSMT4Dnissaidtobesymmetricdeterminant,provethattheoddorderantisymmetricdeterminantiszero.Proof:byEMBEDEquation.DSMT4EMBEDEquation.DSMT4,i
6、.e.EMBEDEquation.DSMT4ItcanbeexpressedasadeterminantofDnEMBEDEquation.DSMT4ThedeterminantofthenatureofEMBEDEquation.DSMT4EMBEDEquation.DSMT4EMBEDEquation.DSMT4EMBEDEquation.DSMT4Whennisodd,Dn=DnandDn=0..3.triangulardeterminantIfwecanputadeterminantthroughappropriatetransformationintoatriang
7、le,theresultistheproductofdeterminantannb.Thistriangleisanimportantmethodinthecalculationofdeterminant.3casesofnorderdeterminantcalculationEMBEDEquation.DSMT4Solution:Thisisthedeterminantofthecharacteristicsofeachrow(column)andelementsareequal,accordingt
