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1、江西财经大学07—08学年第一学期期末考试试卷试卷代码：12063A授课课时：48课程名称：LinearAlgebra适用对象：2006级国际学院1・FillingInTheBlanks(3'x5=15，)XyJ⑴yJX=2(%+y)(-x2・)?+小‘)x+yXy(2)LetAbe(ziXw)matrix,ifAX=0hasuniquesolution,thenthesolutionofadj(A)X=0isX=0hasnonzerosolutions,then1or2kx、+x2+=0(3)I
2、fthesystemofequations112>.Thenthecrossproductaxfl=32.Therearefourchoicesineachquestion,butonlyoneiscorrect.Youshouldchoosethecorrectonein
3、totheblank.(3,X5=15，)2-10(1)Let1x-2=0,thenx=C3-12A.-2B.2C.-1D.1⑵LetAandBbe(nXn)matrices,thenC•A.AB=0A=0orB=0B.ABHOnAHOandBH0C.AB二On
4、A
5、=0or
6、B
7、=0D.AB#0=>AHOandBH0⑶LetS={ai9a29a^}bealinearlydependentsetofvectors,whereax=(1,4,3)j^2=(2,A:,-l),a3=(-2,34)•Th
8、enthenumberkisDA.-1B.1C.3D.-3(4)LetAbe(mxn)matrix,thenthestatementBistrue.A.IfAX=0hasonlysolution,thenAX=bhasonlysolutionB.IfAX=bhasonlysolution,thenAX=0hasonlysolutionC.IfAX=0hasinfinitelymanysolutions,thenAX=bhasinfinitelymanysolutionsA.IfAX=bhasnos
9、olutions,thenAX=0hasnosolutions.(2)IfAis(wXn)matrix,aretwoeigenvaluesofA,andctl9a2aretheeigenvectorscorrespondingto,A2，respectively.ThenD•A.when右=22,beproportionalB.when,=A2,C.when工人，ai9a2mustbenotproportionala、皿2mustbeproportionala^Mmustbenotproporti
10、onal30403.(129LetA=22220-70053-22D.when人工人，，Ayisthecofactorofa{j,Compute:(1)det(A);(2)A41+A42+A43+Au.Solution:(l)det(A)=72522=336-22(2)^41+A42+A43+A44二02-7+x2-x3+2x4+x5=04・(12JLetthesystemoflinearequationsisandexpressthesolutionsbyvectors.兀3+3x4-x5=0•
11、Solvethissystem11-121・11050・11000・Solution:A=0013-1T0013-1T0010-100212000-5000010Thesolutionsare■-1-ro_100+兀510001,兀2,兀5areanyrealnumbers■1005.(12，)LetA=01/23/20■15/2matrixofA.Compute:A3,whereadj(A)istheadjointSolution:A~l=004-2(adj(A)Yldet(A)-~4A--40
12、00-2-40-6-1010111/8191/8A3=043/8074/86.(12，)Thereare(3x3)matricesAandBsuchthatA+B-AB(1)ShowthatmatrixA-Iisinvertible,whereIisanidentitymatrix;1-30_(2)IfmatrixB=210,FindmatrixA.002_Solution:(1)becauseA+B=AB,A=(A-I)B,I+A-I=(A-I)B,(A-I)(B-I)=I,so
