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试卷代号1080中央广播电视大学2011~2012学年度第一学期“开放本科”期末考试(半开卷)工程数学本试题
一、单项选择题每小题3分,共15分1.设,为三阶可逆矩阵,且,则下列( )成立.A.B.C.D.2.设是n阶方阵,当条件()成立时,n元线性方程组有惟一解.AE3.设矩阵的特征值为0,2,则的特征值为()A.0,2B.0,6C.0,0D.2,64.若随机变量,则随机变量.5.对正态总体方差的检验用.
二、填空题每小题3分,共15分6.设均为二阶可逆矩阵,则 .8.设A,B为两个事件,若则称A与B .9.若随机变量,则 .10.若都是的无偏估计,且满足 ______ ,则称比更有效
三、计算题每小题16分,共64分11.设矩阵,,那么可逆吗?若可逆,求逆矩阵.12.在线性方程组中取何值时,此方程组有解在有解的情况下,求出通解
13.设随机变量求和已知,,
14.某切割机在正常工作时,切割的每段金属棒长服从正态分布,且其平均长度为
10.5cm,标准差为
0.15cm从一批产品中随机地抽取4段进行测量,测得的结果如下(单位cm)
10.
410.
610.
110.4问该机工作是否正常()?
四、证明题(本题6分)
15.设n阶矩阵A满足试证A为对称矩阵参考解答
一、单项选择题每小题3分,共15分
1、B
2、A
3、B
4、D
5、C
二、填空题每小题3分,共15分
三、计算题每小题16分,共64分试卷代号1080中央广播电视大学2010~2011学年度第二学期“开放本科”期末考试(半开卷)工程数学本试题2011年7月
一、单项选择题每小题3分,共15分1.设,都是n阶方阵,则等式( )成立.A.B.C.D.2.已知2维向量组则至多是AS()AEA、1B、2C、3D、43.线性方程组解的情况是()A.无解B.有惟一非零解C.只有零解D.有无穷多解4.对任意两个事件A,B,等式成立.A.B.C.D.5.设是来自正态总体的样本,则是统计量.A.B.C.D.
二、填空题每小题3分,共15分1.设AB是3阶方阵,其中则 .2.设A为n阶方阵,若存在数和非零n维向量,使得,则称为A的 ______3.若,则 .4.设随机变量,若则 .5.若参数的两个无偏估计量和满足,则称比更 ______ .
三、计算题每小题16分,共64分1.设矩阵,求.2.设齐次线性方程组,为何值时,方程组有非零解?在有非零解时求其通解
3.设求1;
(2)
4.某钢厂生产了一批管材,每根标准直径100mm,今对这批管材进行检验,随机取出9根测得直径的平均值为
99.9mm,样本标准差s=
0.47,已知管材直径服从正态分布,问这批管材的质量是否合格?(检验显著性水平)
四、证明题(本题6分)设A是可逆的对称矩阵,试证也是对称矩阵参考答案
一、单项选择题每小题3分,共15分
1、C
2、B
3、A
4、D
5、B
二、填空题每小题3分,共15分1.122.特征值3.
0.34.
35.有效
三、计算题每小题16分,共64分
四、证明题(本题6分)试卷代号1080中央广播电视大学2010~2011学年度第一学期“开放本科”期末考试(半开卷)工程数学本试题2011年1月
一、单项选择题每小题3分,共15分1.设,都是n阶方阵,则下列等式成立的是( ).A.B.C.D.2.方程组相容的充分必要条件是AS(),其中.AE3.下列命题中不正确的是()A.有相同的特征多项式B.若是A的特征值,则的非零解向量必是A对应于的特征向量C.若是A的一个特征值,则AX=O必有非零解D.A的特征向量的线性组合仍为A的特征向量4.若事件A与B互斥,则下列等式中正确的是.5.设是来自正态总体的样本,则检验假设采用统计量.
二、填空题每小题3分,共15分6.设,则的根是 .7.设4元钱性方程提AX=B有解且,那么的相应齐次方程程的基础解系含有 ________个解向量8.设A,B互不相容,且PAO,则 .9.设随机变量,则 .10.若样本来自总体,且,则 ______ .
三、计算题每小题16分,共64分11.设矩阵,求.12.求下列线性方程组的通解
13.设随机变量试求1;
(2)使成立的常数已知,,
14.从正态总体中抽取容量为625的样本,计算样本均值得,求的置信区间度为,99%的置信区间(已知)
四、证明题(本题6分)
15.设n阶矩阵A满足则A为可逆矩阵参考解答
一、单项选择题每小题3分,共15分
1、A
2、B
3、D
4、A
5、C
二、填空题每小题3分,共15分1.1-
12.-22.33.04.np
5.
三、计算题每小题16分,共64分试卷代号1080中央广播电视大学2009~2010学年度第二学期“开放本科”期末考试(半开卷)工程数学本试题2010年7月
一、单项选择题每小题3分,共15分1.设,B都是n阶方阵,则下列命题正确的是( ).A.B.C.D.2.向量组的秩是AS().AEA.1B.3C.2D.43.n元线性方程组,有解的充分必要条件是()A.B.A不是行满秩矩阵C.D.4.袋中有3个红球,2个白球,第一次取出一球后放回,第二次再取一球,则两球都是红球的概率是.A.B.C.D.5.设是来自正态总体的样本,则是无偏估计.A.B.C.D.
二、填空题每小题3分,共15分1.设均为3阶方阵,且 .2.设为阶方阵,若存在数和非零维向量,使得 ___,则称为的特征值.3.设随机变量,则 .4.设为随机变量,已知,此时 .5.设是未知参数的一个无偏估计量,则有 ______ .
三、计算题每小题16分,共64分1.设矩阵,且有,求.2.求线性方程组的全部解
3.设试求
(1);
(2)已知,,
4.据资料分析,某厂生产的一批砖,其抗断强度,今从这批砖中随机地抽取了9块,测得抗断强度(单位)的平均值为
31.12,问这批砖的抗断强度是否合格?
四、证明题(本题6分)设是n阶对称矩阵,试证也是对称矩阵参考解答
一、单项选择题每小题3分,共15分
1、A
2、B
3、A
4、D
5、C
二、填空题每小题3分,共15分1.-182.3.
0.34.
275.
三、计算题每小题16分,共64分1.解利用初等行变换得2.解将方程组的增广矩阵化为阶梯形试卷代号1080中央广播电视大学2009~2010学年度第一学期“开放本科”期末考试(半开卷)工程数学本试题2010年1月
一、单项选择题每小题3分,共15分1.设为对称矩阵,则条件( )成立.A.B.C.D.2.AS().AEA.B.C.D.3.若成立,则元方程组有唯一解A.B.C.D.的行向量组线性无关4.若条件成立,则随机事件互为对立事件.A.B.C.D.5.对来自正态总体的一组样本,记,则下列各式中不是统计量.A.B.C.D.
二、填空题每小题3分,共15分6.设均为3阶方阵,且 .7.设为阶方阵,若存在数和非零维向量,使得 ___,则称为相应于特征值的特征向量.8.若,则 .9.如果随机变量的期望且,那么 .10.不含未知参数的样本函数称为 ______ .
三、计算题每小题16分,共32分11.设矩阵,求.12.当取何值时,线性方程组有解,在有解的情况下求出此方程组的一般解.
四、计算分析题(每小题16分,共32分)
13.设试求
(1);
(2)已知,,
14.某车间生产滚珠,已知滚珠直径服从正态分布,今从一批产品里随机取出9个,测得直径平均值为
15.1mm,若已知这批滚珠直径的方差为,试找出滚珠直径均值的置信度为
0.95的置信区间
五、证明题(本题6分)
15.设随机事件相互独立,试证也相互独立参考解答
一、单项选择题每小题3分,共15分
1、B
2、D
3、A
4、C
5、C
二、填空题每小题3分,共15分6.87.8.
0.39.2010.统计量
三、计算题每小题16分,共64分11.解利用初等行变换得12.解将方程组的增广矩阵化为阶梯形
四、计算分析题(每小题16分,共32分)请您删除一下内容,O∩_∩O谢谢!!!【Chinas10must-seeanimations】TheChineseanimationindustryhasseenconsiderablegrowthinthelastseveralyears.Itwentthroughagoldenageinthelate1970sand1980swhensuccessivelybrilliantanimationworkwasproduced.Hereare10must-seeclassicsfromChinasanimationoutpouringthatarenottobemissed.Letsrecallthesecolorfulimagesthatbroughtthecountrygreatjoy.CalabashBrothersCalabashBrothersChinese:葫芦娃isaChineseanimationTVseriesproducedby Shanghai Animation Film Studio.Inthe1980stheserieswasoneofthemostpopularanimationsinChina.ItwasreleasedatapointwhentheChineseanimationindustrywasinarelativelydownedstatecomparedtotherestoftheinternationalcommunity.Stilltheserieswastranslatedinto7differentlanguages.Theepisodeswereproducedwithavastamountofpaper-cutanimations.BlackCatDetectiveBlackCatDetectiveChinese:黑猫警长isaChineseanimationtelevisionseriesproducedbytheShanghaiAnimationFilmStudio.ItissometimesknownasMr.Black.Theserieswasoriginallyairedfrom1984to
1987.InJune2006arebroadcastingoftheoriginalserieswasannounced.Criticsbemoantheseriesviolenceandlackofsuitabilityforchildrenseducation.Proponentsoftheshowclaimthatitismerelyforentertainment.EffendiEffendimeaningsirand teacherinTurkishistherespectfulnameforpeoplewhoownwisdomandknowledge.TheherosrealnamewasNasreddin.Hewaswiseandwittyandmoreimportantlyhehadthecouragetoresisttheexploitationofnoblemen.Hewasalsofullofcompassionandtriedhisbesttohelppoorpeople.AdventureofShukeandBeita【舒克与贝塔】AdventureofShukeandBeitaChinese:舒克和贝塔isaclassicanimationbyZhengYuanjiewhoisknownasKingofFairyTalesinChina.ShukeandBeitaaretwomicewhodontwanttostealfoodlikeothermice.ShukebecameapilotandBeitabecameatankdriverandthepairmetaccidentallyandbecamegoodfriends.ThentheybefriendedaboynamedPipilu.WiththehelpofPiPilutheyco-foundedanairlinenamedShukeBeitaAirlinestohelpotheranimals.Althoughthereareonly13episodesinthisseriesthecontentisverycompactandattractive.Theanimationshowsthepreciousnessoffriendshipandhowpeopleshouldbebravewhenfacingdifficulties.Evenadultsrecallingthisanimationtodaycanstillfeeltouchedbysomescenes.SecretsoftheHeavenlyBookSecretsoftheHeavenlyBookChinese:天书奇谈 alsoreferredtoasLegendoftheSealedBookorTalesabouttheHeavenlyBookwasreleasedin
1983.Thefilmwasproducedwithrigorousdubbingandfluidcombinationofmusicandvividanimations.ThestoryisbasedontheclassicliteraturePingYaoZhuanmeaningTheSuppressionoftheDemonsbyFengMenglong.Yuangongthedeaconopenedtheshrineandexposedtheholybooktothehumanworld.Hecarvedthebookscontentsonthestonewallofawhitecloudcaveinthemountains.Hewasthenpunishedwithguardingthebookforlifebythejadeemperorforbreakingheavenslaw.Inordertopassthisholybooktohumanbeingshewouldhavetogetbytheantagonistfox.ThewholeanimationischaracterizedbycharmingChinese paintingincludingpavilionsancientarchitectureripplingstreamsandcrowdedmarketswhichfullydemonstratetheuniquebeautyofChinasnaturalscenery.PleasantGoatandBigBigWolf【喜洋洋与灰太狼】PleasantGoatandBigBigWolfChinese:喜羊羊与灰太狼isaChineseanimatedtelevisionseries.TheshowisaboutagroupofgoatslivingontheGreenPastureandthestoryrevolvesaroundaclumsywolfwhowantstoeatthem.Itisapopulardomesticanimationseriesandhasbeenadaptedinto movies.NezhaConquerstheDragonKing(Chinese:哪吒闹海) isanoutstandinganimationissuedbytheMinistryofCulturein1979andisbasedonanepisodefromtheChinesemythologicalnovelFengshenYanyi.Amothergavebirthtoaballoffleshshapedlikealotusbud.ThefatherLiJingchoppedopentheballandbeautifulboyNezhasprungout.OnedaywhenNezhawassevenyearsoldhewenttothenearbyseashoreforaswimandkilledthethirdsonoftheDragonKingwhowaspersecutinglocalresidents.ThestoryprimarilyrevolvesaroundtheDragonKingsfeudwithNezhaoverhissonsdeath.ThroughbraveryandwitNezhafinallybrokeintotheunderwaterpalaceandsuccessfullydefeatedhim.ThefilmshowsvariouskindsofattractivesceneriesandthetraditionalcultureofChinasuchasspectacularmountainselegantseawavesandexquisiteancientChineseclothes.Ithasreceivedavarietyofawards.HavocinHeavenThestoryofHavocinHeaven(Chinese:大闹天宫)isbasedontheearliestchaptersoftheclassicstory JourneytotheWest.ThemaincharacterisSunWukongakatheMonkeyKingwhorebelsagainsttheJadeEmperorofheaven.Thestylizedanimationanddrumsandpercussionaccompanimentusedinthisfilmareheavilyinfluencedby Beijing Operatraditions.ThenameofthemoviebecameacolloquialismintheChineselanguagetodescribesomeonemakingamess.RegardlessthatitwasananimatedfilmitstillbecameoneofthemostinfluentialfilmsinallofAsia.CountlesscartoonadaptationsthatfollowedhavereusedthesameclassicstoryJourneytotheWestyetmanyconsiderthis1964iterationtobethemostoriginalfittingandmemorableTheGoldenMonkeyDefeatsaDemon【金猴降妖】TheGoldenMonkeyDefeatsaDemonChinese:金猴降妖alsoreferredasTheMonkeyKingConquerstheDemonisadaptedfromchaptersoftheChineseclassicsJourneytotheWestorMonkeyintheWesternworld.Thefive-episodeanimationseriestellsthestoryofMonkeyKingSunWukongwhofollowedMonkXuanZangstriptotheWesttotaketheBuddhisticsutra.Theymetawhiteboneevilandtheeviltransformedhumanappearancesthreetimestoseducethemonk.TwiceMonkeyKingrecognizeditandbroughtitdown.ThemonkwasunabletorecognizethemonsterandexpelledSunWukong.XuanZangwasthencapturedbythemonster.FortunatelyBajieanotherapprenticeofXuanZangescapedandpersuadedtheMonkeyKingtocomerescuethemonk.FinallySunkillstheevilandsavesXuanZang.Theoutstandinganimationhasreceivedavarietyofawardsincludingthe6thHundredFlowersFestivalAwardandtheChicagoInternationalChildrensFilmFestivalAwardin
1989.McDull【麦兜】McDullisacartoonpigcharacterthatwascreatedin HongKong byAliceMakandBrianTse.AlthoughMcDullmadehisfirstappearancesasasupportingcharacterintheMcMugcomicsMcDullhassincebecomeacentralcharacterinhisownrightattractingahugefollowinginHongKong.ThefirstMcDullmovieMcMugStoryMyLifeasMcDulldocumentedhislifeandtherelationshipbetweenhimandhismother.TheMcMugStoryMyLifeasMcDullisalsobeingtranslatedintoFrenchandshowninFrance.InthisversionMakBingisthemotherofMcDullnothisfather..。