线性代数英文试卷(习题)

第1页共3页ZheJiangUniversityOfScienceAndTechnologyCivilEngineering14FinalTestLinearAlgebraFinalTest(15.06)Cautions:[1]Youareallowedtofinishthistestwithin60minutes.[2]Filltheanswerinthequestionpaperinpart.11.FillingBlanks(45points)[1]figureoutthevalueofthefollowingdeterminantA=yyxyxyyxyxxx______________[2]Herearetwomatrix,TTBA021001,412103,pleasefindAB=____________,BA=______________.[3]AknownmatrixBsatisfiesthefollowingequation,B2-B-2E=0,ifB,B+2Earenonsingular,thus(B+2E)-1=___________[4]Pickupthevectorswhicharelinearlyindependent__________①(-2,1)T,(1,3)T,(2,4)T②2,x2,x,2x+3③x+2,x+1,x2-1④(1,2)T,(-1,1)T[5]11334221tA.ifBisanonzero3x3matrix,AB=0,thust=________[6]|A|=|B|=|C|=2,andthey’reall3*3matrix,findthevalueofD=CB)(AO132=____________[7]Judgewhether400050352400250002BA，havethesameeigenvalues______(‘Y’OR’N’),ifyes,pleasefindthem=_____________[8]findmatrixX,whichsatisfiestheequation11212412X,X=___________[9]findtheeigenvectorsofA=8105,______________________2.Solveproblems(55points)[1]A,Bare3x3matrix,andtheysatisfytheequation2ABAB，and002040200B，findAE.[2]If1221A，findamatrixU，making1UAUexist.(Tip:isadiagonalmatrix).姓名：学号：班级：第2页共3页ZheJiangUniversityOfScienceAndTechnologyCivilEngineering14FinalTest[3]Theequationis1234123412342132344352xxxxxxxxxxxx,finditsgeneralsolution;[4]A=1000410000340043find1Aand*A.[5]101isoneofeigenvectorsofmatrix1111111Amn，（1）findtheeigenvalueα,thenfigureoutthevalueofm,n；（2）JudgewhethermatrixAcanbediagonalizable;ifyes,pleasefindamatrixU,making1UAUexist.(Tip:isadiagonalmatrix).[6]Thearrayofvectorsβ,αaregiven,1231110,,120mn,12111,213.Theyhavethesamerankofmatrix,meanwhile,3islinearlyindependentwith1,2，findthevalueof,mn.-----------------------------------------------DraftpaperArea--------------------------------------------第3页共3页ZheJiangUniversityOfScienceAndTechnologyCivilEngineering14FinalTestAnswerofLinerAlgebra(2015.06)1.Fillingblanks(eachquestionwith5marks)1.2xy(x+y)2.206412103,11005BAAB3.-0.25(A-3E)4.[4]5.t=-36.27/87.Y2,5,48.05.015.1X9.(-3,1)T,(0,1)T2.Solvequestions(eachquestionwith8-10marks)1.A-E=2(B-2E)-1(FINDTHEEXACTANSWERBYYOURSELF)2.U=1105.03.7975100075000076747101βαX4.111BOOCAA*=|A|xA-15.[1]Eigenvalueis2,m=n=1[2]Uconsistsof3eigenvectorswhoseeigenvalueare1.2.-26.M=2,n=1