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大小:1.81 MB
页数:213页
时间:2019-03-04
《Answers to Exercises Linear Algebra by Jim Hefferon.pdf》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、AnswerstoExercisesLinearAlgebraJimHefferon¡¢13¡¢21¯¯¯12¯¯¯¯31¯¡¢1x1¢3¡¢21¯¯¯x¢12¯¯¯¯x¢31¯¡¢68¡¢21¯¯¯62¯¯¯¯81¯NotationRrealnumbersNnaturalnumbers:f0;1;2;:::g¯Ccomplexnumbersf:::¯:::gsetof...suchthat...h:::isequence;likeasetbutordermattersV;W;Uvectorspaces~v;~wvectors~0,~0Vzerovector,zerovectorofVB;
2、DbasesE=h~e;:::;~eistandardbasisforRnn1n¯;~~±basisvectorsRepB(~v)matrixrepresentingthevectorPnsetofn-thdegreepolynomialsMn£msetofn£mmatrices[S]spanofthesetSM©NdirectsumofsubspacesV»=Wisomorphicspacesh;ghomomorphisms,linearmapsH;Gmatricest;stransformations;mapsfromaspacetoitselfT;SsquarematricesRep
3、B;D(h)matrixrepresentingthemaphhi;jmatrixentryfromrowi,columnjjTjdeterminantofthematrixTR(h);N(h)rangespaceandnullspaceofthemaphR1(h);N1(h)generalizedrangespaceandnullspaceLowercaseGreekalphabetnamecharacternamecharacternamecharacteralpha®iota¶rho½beta¯kappa·sigma¾gamma°lambda¸tau¿delta±mu¹upsilon
4、Àepsilon²nuºphiÁzeta³xi»chiÂeta´omicronopsiÃthetaµpi¼omega!Cover.ThisisCramer’sRuleforthesystemx+2y=6,3x+y=8.Thesizeofthefirstboxisthedeterminantshown(theabsolutevalueofthesizeisthearea).Thesizeofthesecondboxisxtimesthat,andequalsthesizeofthefinalbox.Hence,xisthefinaldeterminantdividedbythefirstdeterm
5、inant.TheseareanswerstotheexercisesinLinearAlgebrabyJ.Hefferon.Correctionsorcommentsareverywelcome,emailtojimjoshua.smcvt.eduAnanswerlabeledhereas,forinstance,One.II.3.4,matchesthequestionnumbered4fromthefirstchapter,secondsection,andthirdsubsection.TheTopicsarenumberedseparately.ContentsChapterOne
6、:LinearSystems3SubsectionOne.I.1:Gauss’Method..............................5SubsectionOne.I.2:DescribingtheSolutionSet.......................10SubsectionOne.I.3:General=Particular+Homogeneous.................14SubsectionOne.II.1:VectorsinSpace............................17SubsectionOne.II.2:Length
7、andAngleMeasures......................20SubsectionOne.III.1:Gauss-JordanReduction.......................25SubsectionOne.III.2:RowEquivalence............................27Topic:ComputerAlgebraSystems..............
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