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1、AlgebrathroughpracticeBook4:LinearalgebraAlgebrathroughpracticeAcollectionofproblemsinalgebrawithsolutionsBook4LinearalgebraT.S.BLYTHoE.F.ROBERTSONUniversityofStAndrews-r.Therightf,h,UniversityofCambridgetoprintandsellallmannerofbooksasgrantedbyHenryVlllin1534.The
2、Universityhasprintedandpublishedcontinuouslysince1584.CAMBRIDGEUNIVERSITYPRESSCambridgeLondonNewYorkNewRochelleMelbourneSydneyCAMBRIDGEUNIVERSITYPRESSCambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,SaoPauloCambridgeUniversityPressTheEdinburghBuilding,Cambrid
3、geCB28RU,UKPublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYorkwww.cambridge.orgInformationonthistitle:www.cambridge.org/9780521272896©CambridgeUniversityPress1985Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisionsofrelevant
4、collectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublished1985Re-issuedinthisdigitallyprintedversion2008AcataloguerecordforthispublicationisavailablefromtheBritishLibraryLibraryofCongressCa
5、talogueCardNumber:83-24013ISBN978-0-521-27289-6paperbackContentsPrefaceviBackgroundreferencematerialvii1:DirectsumsandJordanforms12:Dualityandnormaltransformations18SolutionstoChapter131SolutionstoChapter267Testpaper196Testpaper298Testpaper3100Testpaper4102vPrefac
6、eTheaimofthisseriesofproblem-solversistoprovideaselectionofworkedexamplesinalgebradesignedtosupplementundergraduatealgebracourses.Wehaveattempted,mainlywiththeaveragestudentinmind,toproduceavariedselectionofexerciseswhileincorporatingafewofamorechallengingnature.A
7、lthoughcompletesolutionsareincluded,itisintendedthattheseshouldbeconsultedbyreadersonlyaftertheyhaveattemptedthequestions.Inthisway,itishopedthatthestudentwillgainconfidenceinhisorherapproachtotheartofproblem-solvingwhich,afterall,iswhatmathematicsisallabout.Thepr
8、oblems,althougharrangedinchapters,havenotbeen`graded'withineachchaptersothat,ifreaderscannotdoproblemnthisshouldnotdiscouragethemfromattemptingproblemn+
