文档介绍：.(a),(c),and(f)arelinearequationsinx1,x2,andx3.(b)isnotlinearbecauseofthetermxx13.−(d)/(e).(a)and(d)arelinearsystems.(b)isnotalinearsystembecausethefirstandsecondequationsarenotlinear.(c)isnotalinearsystembecausethesecondequationisnotlinear.===−=,(a)and(d)arebothconsistent;x13,xx23221,,x4isasolutionof(a)and====xx121322,,,x3x4isasolutionof(d)..(a),(d),and(e)aresolutions.(b)and(c).(a)75xy−=353xy=+77Lety==+77yt=−+−+=(b)8256xxxx123411531xxxx=−+−12344848===Letxrxs23,,=−+−14848=xr2=xs3=xt4⎡⎤20011.(a)⎢⎥30−correspondsto⎢⎥4⎣⎦⎢⎥011=20x1−=34xx120.=x211Chapter1:SystemsofLinearEquationsandMatricesSSM:ElementaryLinearAlgebra⎡⎤30−(a,b,c)isasolutionofthesystem,then22(b)⎢⎥73−correspondstoax++=bxcy,ax++=bxcy,and⎢⎥14111222⎢⎥07−212++=⎣⎦ax33bxcy3whichsimplymeansthatthe−=++x=−.123+==−−+=,23=⎡⎤−satisfyxlxd+=,thenc−kt+lt=dor(c)73521correspondsto12⎣⎦⎢⎥12401c−d=(k−l)++−=particular,ift=0,thenc=d,andift=1,then72xx1234xx35++=.k=⎡⎤10007====⎢⎥000−(a)True;xx12
xn0willbeasolution.(d)⎢⎥12correspondsto⎢⎥00103⎣⎦⎢⎥00014(b)False;=7x2=−2(c)True;ifk=6thesystemhasinfinitelymany.≠x3=3solutions,whileifk6,=4(d)True;theequationcanbesolvedforonevariable13.(a)Theaugmentedmatrixfor−=26x1intermsoftheother(s),yieldingparametric=38x1equationsthatgiveinfinitelymanysolutions.=−93x1(e)False;thesystem3xy−=−57hasthe⎡⎤−2629xy+=20is⎢⎥38.⎢⎥61014xy−=−⎢⎥93−⎣⎦solutionx=1,y=2.(b)Theaugmentedmatrixfor(f)False;multiplyinganequationbyanonzero−+=⎡63−14⎤constantcdoesnotchangethesolutionsofthe634xx12x3is⎢⎥.system.−=⎣05−11⎦51xx23(g)True;subtractingoneequationfromanotheris(c)Theaugmente