线代知识点总结

线代知识点总结CHAPTER1LinearEquationsinLinearAlgebla1.1Matrixaugmentedmatrix;coefficientmatrixSolvingaLinearSystemReplacement;interchange;scalingExistencethesystemisconsistentUniquenceThesolutionexistandistheonlyone1.2DefinitionLeadindentry;pivotposition;basicvariable;freevariable;back-substitutionparametricdescriptionsofsolutionsets(解集的参数表示)generalsolutionWheneverasystemisinconsistent,thesolutionsetisempty,evenwhenthesystemhasfreevariables.Inthiscase,thesolutionhasnoparametricrepresentation.THEOREM1EachmatrixisrowequivalenttooneandonlyonereducedechelonmatrixTHEOREM2Alinearsystemisconsistentifandonlyiftherightmostcolumnofaugmentedmatrixisnotapivotcolumn,ifandonlyifanechelonformoftheaugementedmatrixhasnorowoftheform[0……0b]withbnonzeroIfalinearsystemisconsistent,thenthesolutionsetcontainseither(i)Auniguesolution,whentherearenofreevariables,or(ii)Infinitelymanysolutions,whenthereisatleastonefreevaribales1.3子空间的基