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1、ElementaryLinearAlgebrawithApplicationsThispageintentionallyleftblankElementaryLinearAlgebrawithApplicationsNinthEditionBernardKolmanDrexelUniversityDavidR.HillTempleUniversityUpperSaddleRiver,NewJersey07458LibraryofCongressCataloging-in-PublicationDataonfile.EditorialDirector,ComputerSc
2、ience,Engineering,andAdvancedMathematics:MarciaJ.HortonSeniorEditor:HollyStarkEditorialAssistant:JenniferLonscheinSeniorManagingEditor/ProductionEditor:ScottDisannoArtDirector:JuanLopez´CoverDesigner:MichaelFruhbeisArtEditor:ThomasBenfattiManufacturingBuyer:LisaMcDowellMarketingManager:
3、TimGalliganCoverImage:(c)WilliamT.Williams,Artist,1969Trane,1969Acryliconcanvas,108×84.CollectionofTheStudioMuseuminHarlem.GiftofCharlesCowles,NewYork.c2008,2004,2000,1996byPearsonEducation,Inc.PearsonEducation,Inc.UpperSaddleRiver,NewJersey07458Earliereditionsc1991,1986,1982,byKT
4、I;1977,1970byBernardKolmanAllrightsreserved.Nopartofthisbookmaybereproduced,inanyformorbyanymeans,withoutpermissioninwritingfromthepublisher.PrintedintheUnitedStatesofAmerica10987654321ISBN0-13-229654-3PearsonEducation,Ltd.,LondonPearsonEducationAustraliaPTY.Limited,SydneyPearsonEducati
5、onSingapore,Pte.,LtdPearsonEducationNorthAsiaLtd,HongKongPearsonEducationCanada,Ltd.,TorontoPearsonEducaciondeMexico,S.A.deC.V.´PearsonEducation—Japan,TokyoPearsonEducationMalaysia,Pte.LtdToLisa,Stephen,andtothememoryofLillieB.K.ToSuzanneD.R.H.ThispageintentionallyleftblankCONTENTSPrefa
6、cexiTotheStudentxvii1LinearEquationsandMatrices11.1SystemsofLinearEquations11.2Matrices111.3MatrixMultiplication211.4AlgebraicPropertiesofMatrixOperations341.5SpecialTypesofMatricesandPartitionedMatrices421.6MatrixTransformations551.7ComputerGraphics(Optional)631.8CorrelationCoefficient(
7、Optional)73SupplementaryExercises802SolvingLinearSystems862.1EchelonFormofaMatrix862.2SolvingLinearSystems952.3ElementaryMatrices;FindingA−11172.4EquivalentMatrices1262.5LU-Factorization(Optional)130SupplementaryExercises1373Determinants1413.1Definition1413.2PropertiesofDetermin
