还剩7页未读,继续阅读
文本内容:
电大工程数学(本)复习资料考试小抄最新
一、单项选择题(每小题3分,本题共15分)
1.若,则(A ).A.3B.2C.D.
2.已知2维向量组,则至多是(B ). AB CD
3.设为阶矩阵,则下列等式成立的是(C)A.B.C.D.
4.若满足(B ),则与是相互独立.A.B.C.D.
5.若随机变量的期望和方差分别为和,则等式(D)成立.A.B.C.D.6.若是对称矩阵,则等式( B)成立.A.B.C.D.7.(D).A.B.C.D.8.若(A )成立,则元线性方程组有唯一解.A.B.C.D.的行向量线性相关
4.若条件( C)成立,则随机事件,互为对立事件.A.或B.或C.且D.且9.对来自正态总体(未知)的一个样本,记,则下列各式中(C )不是统计量.A.B.C.D.10.设都是n阶方阵,则下列命题正确的是A.A.B.C.D.若,则或11.向量组的秩是(B).A.1B.3C.2D.412.元线性方程组有解的充分必要条件是( A).A.B.不是行满秩矩阵C.D.
13.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(D).A.B.C.D.14.设是来自正态总体的样本,则(C)是无偏估计.A.B.C.D.15.设为阶矩阵,则下列等式成立的是(A ). A.B.C.D.16.方程组相容的充分必要条件是B,其中,. A.B.C.D.17.下列命题中不正确的是(D).A.A与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=0是A的一个特征值,则必有非零解D.A的特征向量的线性组合仍为A的特征向量18.若事件与互斥,则下列等式中正确的是( A ). A. B. C. D.19.设是来自正态总体的样本,则检验假设采用统计量U=( C).A.B.C.D.
二、填空题(每小题3分,共15分)
1.设均为n阶可逆矩阵,逆矩阵分别为,则 .
2.向量组线性相关,则-
1.
3.已知,则 .
0.6
4.已知随机变量,那么
2.4.
5.设是来自正态总体的一个样本,则 .6.设均为3阶方阵,,则 8. 7.设为n阶方阵,若存在数和非零n维向量,使得,则称为相应于特征值的特征向量. 8.若,则
0.3.9.如果随机变量的期望,,那么 20. 10.不含未知参数的样本函数称为 统计量11.设均为3阶方阵,,则 -18. 12.设随机变量,则a=
0.3.13.设为随机变量,已知,此时 27 . 14.设是未知参数的一个无偏估计量,则有 .15.设,则的根是 1,-1,2,-2. 16.设4元线性方程组AX=B有解且r(A)=1,那么AX=B的相应齐次方程组的基础解系含有3个解向量. 17.设互不相容,且,则 0.18.设随机变量X~B(n,p),则E(X)= np. 19.若样本来自总体,且,则 .
三、计算题(每小题16分,共64分)1设矩阵,求
(1),
(2).解
(1)
(2)利用初等行变换得 即
2.当取何值时,线性方程组有解,在有解的情况下求方程组的全部解.解将方程组的增广矩阵化为阶梯形由此可知当时,方程组无解当时,方程组有解 此时相应齐次方程组的一般解为(是自由未知量)分别令及,得齐次方程组的一个基础解系 令,得非齐次方程组的一个特解 由此得原方程组的全部解为(其中为任意常数)
3.设,试求⑴;⑵.(已知)解1 2
4.已知某种零件重量,采用新技术后,取了9个样品,测得重量(单位kg)的平均值为
14.9,已知方差不变,问平均重量是否仍为15()?解零假设.由于已知,故选取样本函数 已知,经计算得, 由已知条件,故接受零假设,即零件平均重量仍为15.5.设矩阵,求.解利用初等行变换得 即 由矩阵乘法得6.当取何值时,线性方程组有解,在有解的情况下求方程组的全部解.解将方程组的增广矩阵化为阶梯形 由此可知当时,方程组无解当时,方程组有解 此时齐次方程组化为分别令及,得齐次方程组的一个基础解系 令,得非齐次方程组的一个特解由此得原方程组的全部解为 (其中为任意常数) 7.设,试求1;2.(已知)解1 2 8.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.解由于已知,故选取样本函数 已知,经计算得 滚珠直径均值的置信度为
0.95的置信区间为,又由已知条件,故此置信区间为9.设矩阵,且有,求.解利用初等行变换得 即 由矩阵乘法和转置运算得 10.求线性方程组的全部解.解将方程组的增广矩阵化为阶梯形 方程组的一般解为 (其中为自由未知量)令=0,得到方程的一个特解.方程组相应的齐方程的一般解为 (其中为自由未知量)令=1,得到方程的一个基础解系.于是,方程组的全部解为(其中为任意常数)11.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kg/cm2)的平均值为
31.12,问这批砖的抗断强度是否合格().解零假设.由于已知,故选取样本函数 已知,经计算得, 由已知条件,故拒绝零假设,即这批砖的抗断强度不合格12.设矩阵,求.解由矩阵乘法和转置运算得 利用初等行变换得即14.求下列线性方程组的通解.解 利用初等行变换,将方程组的增广矩阵化成行简化阶梯形矩阵,即方程组的一般解为,其中,是自由未知量.令,得方程组的一个特解.方程组的导出组的一般解为,其中,是自由未知量.令,,得导出组的解向量;令,,得导出组的解向量.所以方程组的通解为其中是任意实数.15.设随机变量X~N(3,4).求
(1)P(1X7);
(2)使P(Xa)=
0.9成立的常数a.已知,,.解
(1)P(1X7)====
0.9773+
0.8413–1=
0.8186
(2)因为P(Xa)===
0.9所以,a=3+=
5.5616.从正态总体N(,4)中抽取容量为625的样本,计算样本均值得=
2.5,求的置信度为99%的置信区间.已知解已知,n=625,且~ 因为=
2.5,,, 所以置信度为99%的的置信区间为17.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.解由于已知,故选取样本函数 已知,经计算得 滚珠直径均值的置信度为
0.95的置信区间为,又由已知条件,故此置信区间为
四、证明题(本题6分)1设是两个随机事件,试证.证明由事件的关系可知而,故由加法公式和乘法公式可知证毕. 2.设随机事件相互独立,试证也相互独立. 证明所以也相互独立.证毕.3.设是阶对称矩阵,试证也是对称矩阵.证明是同阶矩阵,由矩阵的运算性质可知已知是对称矩阵,故有,即由此可知也是对称矩阵,证毕.4.设n阶矩阵A满足,则A为可逆矩阵.证明因为,即.所以,A为可逆矩阵5.设向量组线性无关,令,,,证明向量组线性无关证明设,即因为线性无关,所以解得k1=0k2=0k3=0,从而线性无关.6.设为随机事件,试证证明由事件的关系可知 而,故由概率的性质可知请您删除一下内容,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..。