D. C. Lay - Linear Algebra and Its Applications - Solutions Manual.pdf

文档介绍：:Thekeyexercisesare7(or11or12),19–22,,thesymbolsR1,R2,…,standforrow1(orequation1),row2(orequation2),+=57−−=−−−−27xx125275xx+=57157ReplaceR2byR2+(2)R1andobtain:12=39x2039xx+=57157ScaleR2by1/3:12=x23013x=−810−8ReplaceR1byR1+(–5)R2:1=x23013Thesolutionis(x1,x2)=(–8,3),orsimply(–8,3).24xx+=−424−4+=57xx12115711xx+=−2212−2ScaleR1by1/2andobtain:12+=57xx12115711xx+=−22122−ReplaceR2byR2+(–5)R1:12−=−321x20321xx+=−2212−2ScaleR2by–1/3:12=−−x27017x=121012ReplaceR1byR1+(–2)R2:1=−−x27017Thesolutionis(x1,x2)=(12,–7),orsimply(12,–7).12CHAPTER1•:xx+=5715712−=−−−xx1222122xx+=57157ReplaceR2byR2+(–1)R1andobtain:12−=−−−79x2079xx+=57157ScaleR2by–1/7:12=x29/7019/7x=4/7104/7ReplaceR1byR1+(–5)R2:1=x29/7019/7Thepointofintersectionis(x1,x2)=(4/7,9/7).:xx−=51151−12−=−37xx125375xx−=51151−ReplaceR2byR2+(–3)R1andobtain:12=82x2082xx−=5115−1ScaleR2by1/8:12=x21/4011/4x=9/4109/4ReplaceR1byR1+(5)R2:1=x21/4011/4Thepointofintersectionis(x1,x2)=(9/4,1/4).“triangular”=–5,,thatmeanstoreplaceR2byitssumwith3timesR3,andthenreplaceR1byitssumwith––3timesR3,which16401−−02704−produces.Afterthat,thenextstepistoscalethefourthrowby–1/5.00123−000515−,thenextstepwouldbetointerchangeR3andR4,,thethirdrowoftheaugmentedmatrixcorrespondstotheequation0x1+0x2+0x3=1,orsimply,0=