INSTRUCTOR
SOLUTIONS
mMANUAL
,INSTRUCTOR’S SOLU m
TIONS MANUAL m
THOMAS POLASKI m
Winthrop University
m
JUDITH MCDONALD
m
Washington State University
m m
LINEAR A LGEBRA m
AND I TS
m m A PPLICATIONS
FOURTH E DITION m
David C. Lay m m
University of Maryland
m m
,Themauthormandmpublishermofmthismbookmhavemusedmtheirmbestmeffortsminmpreparingmthismbook.mThesemeffortsminclude
mthe m development, m research, mand mtesting mofmthe mtheories mand mprograms mto m determine mtheir meffectiveness. m The mauth
ormandmpublishermmakemnomwarrantymofmanymkind,mexpressedmormimplied,mwithmregardmtomthese mprogramsmormthemdo
cumentationmcontainedminmthismbook.mThemauthormandmpublishermshallmnotmbemliableminmanymeventmformincidentalmorm
consequential mdamagesminmconnectionmwith,mormarisingmoutmof,mthemfurnishing, mperformance, mormusemofmthesemprogr
ams.
ReproducedmbymPearsonmAddison-
Wesleymfrommelectronicmfilesmsuppliedmbymthemauthor.mCopyrightm©m2012,m2006,m19
97mPearsonmEducation, mInc.
PublishingmasmPearsonmAddison-Wesley,m75mArlingtonmStreet,mBoston,mMAm02116.
Allmrightsmreserved.mNompartmofmthismpublicationmmaymbemreproduced, mstoredminmamretrievalmsystem,mormtransmitted,
minmany mform morm by many m means,melectronic, mmechanical, mphotocopying, mrecording, m orm otherwise, m without mthe m prior
m written m permission mofm the m publisher. mPrinted m in m the m United mStates mofm America.
ISBN-13:m978-0-321-38888-9
ISBN-10:m0-321-38888-7
1m2m3m4m5m6mBBm15m14m13m12m11
, Contents
CHAPTERm1 LinearmEquationsminmLinearmAlgebram 1
CHAPTERm2 MatrixmAlgebra 87
CHAPTERm3 Determinants 167
CHAPTERm4 VectormSpaces 197
CHAPTERm5 EigenvaluesmandmEigenvectors 273
CHAPTERm6 OrthogonalitymandmLeastmSquares 357
CHAPTERm7 SymmetricmMatricesmandmQuadraticmForms 405
CHAPTERm8 ThemGeometrymofmVectormSpaces 453
iii
SOLUTIONS
mMANUAL
,INSTRUCTOR’S SOLU m
TIONS MANUAL m
THOMAS POLASKI m
Winthrop University
m
JUDITH MCDONALD
m
Washington State University
m m
LINEAR A LGEBRA m
AND I TS
m m A PPLICATIONS
FOURTH E DITION m
David C. Lay m m
University of Maryland
m m
,Themauthormandmpublishermofmthismbookmhavemusedmtheirmbestmeffortsminmpreparingmthismbook.mThesemeffortsminclude
mthe m development, m research, mand mtesting mofmthe mtheories mand mprograms mto m determine mtheir meffectiveness. m The mauth
ormandmpublishermmakemnomwarrantymofmanymkind,mexpressedmormimplied,mwithmregardmtomthese mprogramsmormthemdo
cumentationmcontainedminmthismbook.mThemauthormandmpublishermshallmnotmbemliableminmanymeventmformincidentalmorm
consequential mdamagesminmconnectionmwith,mormarisingmoutmof,mthemfurnishing, mperformance, mormusemofmthesemprogr
ams.
ReproducedmbymPearsonmAddison-
Wesleymfrommelectronicmfilesmsuppliedmbymthemauthor.mCopyrightm©m2012,m2006,m19
97mPearsonmEducation, mInc.
PublishingmasmPearsonmAddison-Wesley,m75mArlingtonmStreet,mBoston,mMAm02116.
Allmrightsmreserved.mNompartmofmthismpublicationmmaymbemreproduced, mstoredminmamretrievalmsystem,mormtransmitted,
minmany mform morm by many m means,melectronic, mmechanical, mphotocopying, mrecording, m orm otherwise, m without mthe m prior
m written m permission mofm the m publisher. mPrinted m in m the m United mStates mofm America.
ISBN-13:m978-0-321-38888-9
ISBN-10:m0-321-38888-7
1m2m3m4m5m6mBBm15m14m13m12m11
, Contents
CHAPTERm1 LinearmEquationsminmLinearmAlgebram 1
CHAPTERm2 MatrixmAlgebra 87
CHAPTERm3 Determinants 167
CHAPTERm4 VectormSpaces 197
CHAPTERm5 EigenvaluesmandmEigenvectors 273
CHAPTERm6 OrthogonalitymandmLeastmSquares 357
CHAPTERm7 SymmetricmMatricesmandmQuadraticmForms 405
CHAPTERm8 ThemGeometrymofmVectormSpaces 453
iii
