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1、线性代数习题解答赵树嫄（LinearalgebraanswersZhaoShuyuan）ExercisesforLinearAlgebra(Zhou3)Instructions:1.TeachingmaterialsZhaoShuyuan.LinearAlgebra(FourthEdition),RenminUniversityofChinapress,19972,theanswerisonlyforreference;ifthereisanerror,lookback.Problemone(A)1,(6)(7)2,7(3)(4)04,or58,(1)4(2),7(
2、3)13(4)N(n(n-1))...21)=(n-1)+(n-2)+...+2+1=10,thecolumnnumberis3k42l,soKandlcanchoose1or5;ifk=1,l=5,N(31425)=3,thek=1,l=5.isnegative;12,(1)anitemnotequaltozero(2)!13,(3)(4)addthecolumnstothefirstcolumn,17,(1)startwiththesecondline,witheachlineplusthefirstline.(2)...(3)thesumofthecolumn
3、sisequal,andeachrowisaddedtothefirstrow...18,(3)20,thefirstlineisaddedtoeachlinetogettheuppertriangledeterminant,21,thesumoftherowsisequal,thecolumnsareaddedtothefirstcolumn,andthecommonfactorisputforwardStartingfromthesecondline,subtractingthefirstrowfromeachrow22,thelastcolumnismulti
4、pliedbyfirstand2,respectively,...TheN-1columngetstheuppertriangledeterminant23,expandinthefirstcolumn24,thefirstcolumnsecondcolumnthirdcolumnsecondcolumn,then,...Columnn,columnn-1,andfinallyexpandinline1..25,(1)(2)thesumofthelinesisequal...(3)similartothe22question...(4)atthattime,subs
5、titutingthedeterminantwouldmakethedeterminanthavetwolinesofthesame,sotheywerealltherootoftheequation.28,29,inwhich1,3,twolinescorrespondtoproportion,soitiszero32,startfromthesecondrowofeachrowismultipliedby(-1)onthelinetothefirstcolumnandthenpressstart33,expandinthefirstcolumn34,thepri
6、mitiveequationistransformedinto....35,=0Solutionor36,(Vandermondedeterminant)37,Xie40,(3)D=63,D1=63,D2=126,D3=189(6)D=20,D1=60,D2=-80,D3=-20,D4=2042dreams.Henceonlythezerosolutionoftheoriginalequation.43order,Whenorwhenthesystemofhomogeneousequationshasnonzerosolutions.44,thecoefficien
7、tdeterminantofthehomogeneoussystemofequationsThatis,thesystemofhomogeneousequationshasonlyzerosolutionsatthesametime.Problemtwo(A)2,(1)(2)(3)(4)3Y=2(A+B)isobtainedby(2A-Y)+2(B-Y)=0L3,becausetheequationsareobtainedThesolutionsarex==5,y==6,u=4,v=-25,(2)(3)14(7)11,(1)set,thenEquationsar
