알기쉬운 선형대수 12판 솔루션 pdf - algiswiun seonhyeongdaesu 12pan sollusyeon pdf

CHAPTER1:SYSTEMSOFLINEAREQUATIONSANDMATRICES

1.1IntroductiontoSystemsofLinearEquations

2.Equationsinpart(a)donotformalinearsystemsincethesecondoneisnotalinearequation.

Equationsinparts(b),(c),and(d)formlinearsystems.

3.(a)Notlinearbecauseoftheterm

x

2

x

3.(b)Linear

4.(b)Wecansolvethissystembyinspectionsincethesecondequationisamultipleofthefirst.

Letting4solvesbothequations,thereforethesystemisconsistent.

(c)Aneasywaytofindanexampleofasolutionofthissystemwouldbebyletting0first,

thenlookforvaluesofandthatsolvetheresultingsystem

4x+2z=–1

–x–3z=0

Adding4timesthesecondequationtothefirstwillyieldasimplifiedsystem

–10z=–1

–x–3z=0

whichissolvedby

and

.Togetherwith0,thisisasolutionoftheoriginal

system,showingittobeconsistent.

(d)Weadd6timesthefirstequationtothethird,thenproceedtoaddthefirstequationto

thefourth,andthesecondonetothefourth,obtainingasimplifiedsystem

34

51

1627

71

Clearly,thelasttwoequationsarecontradictory,thusthesystemisinconsistent.