【线性代数教学资料】13-14线代答案

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1、江西财经大学2013-2014学年第一学期期末考试试卷授课课时：48适用对象：2012级国际学院试卷审核人李杰试卷代码：12063A考试时间110分钟课程名称：LinearAlgebra（主干课程）试卷命题人何明2/271FillingintheBlanks(writedowntheanswerontheanswersheet・3pointsx5(1)讦"a2=4,thenD.=41~a\+2d]2=8a2°22a2l-a2[+2色2=15points)(2)LetAbe(3X3)matrix,andthe

2、n(3A尸(3)LetAbe(3X3)matrix,and-1,0JaretheeigenvaluesofA,andB=24?-2A+/,thenthedeterminantofBB=5(4)Ifa==(l,-2,3^)r，andareorthogonal，then1-132,0=1，7=2121(5)Let<7=•Thenthetripleproductso•(0x力2、Singlechoiceitems(ThereareonlyonechoiceiscorrectsYoushouldchoosethecorre

3、ctoneontheanswersheet.3pointsX5=15points)Ax+y+z=0(1)Ifthesystemofequations

4、・

5、即c.-3国・

6、即B.-3

7、Ar

8、-

9、B

10、D.(—3)2”

11、外0(3)SupposeA.Bareall(nx/?)matr

12、ix,ifA^0butBA=0,then(D)<4-2>2、A.B.i1一1丿-1;z7<-1-2、r4C.D・<14丿,一2-LC.(A+B)2=A2+B2D.(4)LetA=It2、4>thentheadjointmatrixA"=(A(5)SupposeAhaveaeigenvalue(B)A.-AkC.kAisaeigenvalueofainvertiblematrixA.then(M)"1(kH0)mustB・丄kAD上A3、Thecalculationproblem(writethedetailedc

13、alculationstepsandresultsontheanswersheet,12points)Evaluatethe4x4determinant1211111-21=2-30-3二=-4-3000-232122121213131431222211000613121-3011003-2-3-24points8points=-4x3=一1212points4、Thecalculationproblem(writethedetailedcalculationstepsandresultsontheanswersh

14、eet,12points)<-l00>〜300、LetA=1-10evaluate(A+2/)»(A—21)=4-301-1丿/<-44—3)/r-i00、<200、<-300、(A-2Z)=i-10—020—1-30~9points1-b02}71-3丿r-300>(A+2Z)~1(A-2Z)=4-30]2points<-44一3丿0()>0()、(100)(A+2/)=1-10+020二11001__1<002丿011j7X7X/<100>-1ri00、(A+2Z)-1:110=-i10<01［丿-1b3poi

15、nts6points5Thecalculationproblem(writethedetailedcalculationstepsandresultsontheanswersheet,12points)1LetA=2-123-2541-107a.FindabasisforthecolumnspaceofAconsistingofcolumnsofA"1-123~1-107_2-254T001-21-10700004points(2、So7?(A)=$p{25}丄6pointsb.FindabasisforN(A)

16、xx=x2+7兀4lOpoints0SoN(A)=sp{12points6Thecalculationproblem(writethedetailedcalculationstepsandresultsontheanswersheet,12points)Solvethegivensystemoflinearequations.X]+2x2v+6x2-x3-