Student Solutions Manual for ELEMENTA
t t t t
RY LINEAR ALGEBRASIXTH EDITIO
t t t t
N
Larson
Houghton Mifflin Harcourt Publishing Company
t t t t
Boston New York
t
,Publisher:tRichardtStratton
SeniortSponsoringtEditor:tCathytCantint
MarketingtManager:tJennifertJonestDev
elopmenttEditor:tJaninetTangneytAssoci
atetEditor:tJeanninetLawlesstProjecttEdit
or:tKerrytFalvey
NewtTitletProjecttManager:tPattO’Neill
Copyrightt©t2009tbytHoughtontMifflintHarcourttPublishingtCompany.tAlltrightstreserved.
Notparttoftthistworktmaytbetreproducedtorttransmittedtintanytformtortbytanytmeans,telectronictortmechanical,tincludin
gtphotocopyingtandtrecording,tortanytinformationtstoragetortretrievaltsystemtwithouttthetpriortwrittentpermissiontoftH
oughtontMifflintHarcourttPublishingtCompanytunlesstsuchtcopyingtistexpresslytpermittedtbytfederaltcopyrighttlaw.t
AddresstinquiriesttotCollegetPermissions,tHoughtontMifflintHarcourttPublishingtCompany,t222tBerkeleytStreet,tBost
on,tMAt02116-3764.
PrintedtintthetUnitedtStatestoftAmerica.tI
SBNt13:t978-0-618-78377-9
ISBNt10:t0-618-78377-6
123456789-???-12t11t10t09
, PREFACE
ThistStudenttSolutionstManualtistdesignedtastatsupplementttotElementarytLineartAlgebra,tSixthtEdition,tbytRontLarsontandtDav
idtC.tFalvo.tAlltreferencesttotchapters,ttheorems,tandtexercisestrelatettotthetmainttext.tSolutionsttoteverytodd-
numberedtexercisetintthettexttaretgiventwithtalltessentialtalgebraictstepstincluded.tAlthoughtthistsupplementtistnottatsubstitutetfo
rtgoodtstudythabits,tittcantbetvaluabletwhentincorporatedtintotatwell-plannedtcoursetoftstudy.
Wethavetmadeteveryteffortttotseetthattthetsolutionstaretcorrect.tHowever,twetwouldtappreciatethearingtabouttanyterrorstortothe
rtsuggestionstfortimprovement.tGoodtlucktwithtyourtstudytoftelementarytlineartalgebra.
RontLarsontLarso
ntTexts,tInc.
iii
, CONTENTS
Chaptert1 SystemstoftLineartEquations. ............................................................ 1
Chaptert2 Matrices ......................................................................................... 26
Chaptert3 Determinants ................................................................................. 63
Chaptert4 VectortSpaces................................................................................. 96
Chaptert5 InnertProducttSpaces .................................................................... 137
Chaptert6 LineartTransformations ................................................................ 185
Chaptert7 EigenvaluestandtEigenvectors ...................................................... 219
iv
t t t t
RY LINEAR ALGEBRASIXTH EDITIO
t t t t
N
Larson
Houghton Mifflin Harcourt Publishing Company
t t t t
Boston New York
t
,Publisher:tRichardtStratton
SeniortSponsoringtEditor:tCathytCantint
MarketingtManager:tJennifertJonestDev
elopmenttEditor:tJaninetTangneytAssoci
atetEditor:tJeanninetLawlesstProjecttEdit
or:tKerrytFalvey
NewtTitletProjecttManager:tPattO’Neill
Copyrightt©t2009tbytHoughtontMifflintHarcourttPublishingtCompany.tAlltrightstreserved.
Notparttoftthistworktmaytbetreproducedtorttransmittedtintanytformtortbytanytmeans,telectronictortmechanical,tincludin
gtphotocopyingtandtrecording,tortanytinformationtstoragetortretrievaltsystemtwithouttthetpriortwrittentpermissiontoftH
oughtontMifflintHarcourttPublishingtCompanytunlesstsuchtcopyingtistexpresslytpermittedtbytfederaltcopyrighttlaw.t
AddresstinquiriesttotCollegetPermissions,tHoughtontMifflintHarcourttPublishingtCompany,t222tBerkeleytStreet,tBost
on,tMAt02116-3764.
PrintedtintthetUnitedtStatestoftAmerica.tI
SBNt13:t978-0-618-78377-9
ISBNt10:t0-618-78377-6
123456789-???-12t11t10t09
, PREFACE
ThistStudenttSolutionstManualtistdesignedtastatsupplementttotElementarytLineartAlgebra,tSixthtEdition,tbytRontLarsontandtDav
idtC.tFalvo.tAlltreferencesttotchapters,ttheorems,tandtexercisestrelatettotthetmainttext.tSolutionsttoteverytodd-
numberedtexercisetintthettexttaretgiventwithtalltessentialtalgebraictstepstincluded.tAlthoughtthistsupplementtistnottatsubstitutetfo
rtgoodtstudythabits,tittcantbetvaluabletwhentincorporatedtintotatwell-plannedtcoursetoftstudy.
Wethavetmadeteveryteffortttotseetthattthetsolutionstaretcorrect.tHowever,twetwouldtappreciatethearingtabouttanyterrorstortothe
rtsuggestionstfortimprovement.tGoodtlucktwithtyourtstudytoftelementarytlineartalgebra.
RontLarsontLarso
ntTexts,tInc.
iii
, CONTENTS
Chaptert1 SystemstoftLineartEquations. ............................................................ 1
Chaptert2 Matrices ......................................................................................... 26
Chaptert3 Determinants ................................................................................. 63
Chaptert4 VectortSpaces................................................................................. 96
Chaptert5 InnertProducttSpaces .................................................................... 137
Chaptert6 LineartTransformations ................................................................ 185
Chaptert7 EigenvaluestandtEigenvectors ...................................................... 219
iv
