线代知识点总结.docx

《线代知识点总结.docx》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、线代知识点总结CHAPTER1LinearEquationsinLinearAlgebla1.1Matrixaugmentedmatrix;coefficientmatrixSolvingaLinearSystemReplacement;interchange;scalingExistencethesystemisconsistentUniquenceThesolutionexistandistheonlyone1.2DefinitionLeadindentry;pivotposition;basicvariable;freevar

2、iable;back-substitutionparametricdescriptionsofsolutionsets(解集的参数表示)generalsolutionWheneverasystemisinconsistent,thesolutionsetisempty,evenwhenthesystemhasfreevariables.Inthiscase,thesolutionhasnoparametricrepresentation.THEOREM1Eachmatrixisrowequivalenttooneandonlyone

3、reducedechelonmatrixTHEOREM2Alinearsystemisconsistentifandonlyiftherightmostcolumnofaugmentedmatrixisnotapivotcolumn,ifandonlyifanechelonformoftheaugementedmatrixhasnorowoftheform[0……0b]withbnonzeroIfalinearsystemisconsistent,thenthesolutionsetcontainseither(i)Aunigues

4、olution,whentherearenofreevariables,or(ii)Infinitelymanysolutions,whenthereisatleastonefreevaribales1.3子空间的基