2015年电大工程数学复习资料(本）期末复习考试试题资料小抄

电大工程数学复习资料一、线性代数1、矩阵的初等行变换1）两行互换，2）某一行乘以一个非零常数，3）某一行的K倍加到另一行。2、阶梯型矩阵1）全为0的行写在最下面，2）首非零元的列标随行标的增大而增大。如230146523、行简化阶梯型矩阵满足下列条件的阶梯型矩阵1）首非零元全为1，2）首非零元所在列其余元素全为0。如02543104、求矩阵A的秩A阶梯型矩阵。阶梯型矩阵非零行的行数既为矩阵A的秩即RA初等行变换例设矩阵，求矩阵的秩151233897A解用初等行变换将矩阵化为阶梯形681403722587931152151207430由此可知矩阵的秩为25、求矩阵方程AXB（AB）IX或XB初等行变换1A求矩阵A的逆矩阵（AI）（I）初等行变换11例设矩阵A,B,求AB或解矩阵方程AXB3210501解（AB）503215043211041218BA15208例设矩阵，求,1032A1A解10I10102/31032所以102/31A6、N元线性方程组解的判定1）AXBRABRA时，方程组有解个自由未知量时，有无穷多解，且有时，方程组有唯一解RNNRABRRABRA时，方程组无解AX0方程组一定有解个自由未知量时，有非零解，且有时，方程组有唯一零解RNNRA2）求齐次线性方程组AX0的基础解系将方程组中的自由未知量分别取（K，0，0）,0,K,0,0,0,K形式所得到的解向量3）求AX0的一般解和全部解方程组的全部解基础解系方程组的一般解行简化阶梯型矩阵初等行变换A求AXB的一般解和全部解方程组的全部解原方程组的一个特解解系相应齐次方程组的基础方程组的一般解行简化阶梯型矩阵初等行变换B例设齐次线性方程组的系数矩阵经过初等行变换，得0AX0231A求此齐次线性方程组的一个基础解系和通解解因为0012/31023得一般解（其中是自由元）4321X43,X令，得；0,43X021X令，得12所以，是方程组的一个基础解系21,X方程组的通解为，其中是任意常数21K21,K例2线性方程组的全部解26240833143XX解（AB）21621408308521130123854方程组的一般解将常数项视为零，取得00651984325689X14X相应齐次方程组的一个基础解系，取原方程组的一个特解故方程组的全部解15804X0691XC069158例当取何值时，线性方程X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190205121479631210584910051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432159XX分别令及，得齐次方程组的一个基础解系340,1,105,1921XX令，得非齐次方程组的一个特解X34,080由此得原方程组的全部解为（其中为任意常数）XKX012K12,二、概率部分1、假设为两事件，已知，求BA,40,60,5ABPAPBP解240PB70APA2、正态分布X,2N,PXB1P（X196UN91532故认为这批砖的抗断强度不合格例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，测得它们直径的平均值为999MM,样本标准差S047,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005，）3062805T解假设H100已知N9S047999X30628470319NST故认为这批管材的质量是合格的请您删除一下内容，O_O谢谢2015年中央电大期末复习考试小抄大全，电大期末考试必备小抄，电大考试必过小抄AFTEREARNINGHISSPURSINTHEKITCHENSOFTHEWESTIN,THESHERATON,SENSONTHEBUND,ANDASPRINKLINGOFOTHERTOPNOTCHVENUES,SIMPSONLUFINALLYGOTTHECHANCETOBECOMEHISOWNBOSSINNOVEMBER2010SORTOFTHESHANGHAIBORNCHEFMIGHTNOTACTUALLYOWNCALIFORNIAPIZZAKITCHENCPKBUTHEISINSOLECHARGEOFBOTHKITCHENANDFRONTOFHOUSEATTHISSINANMANSIONSSTALWART“ITSCERTAINLYARESPONSIBILITYTOBETHEHEADCHEF,ANDTHENTOHAVETOMANAGETHERESTOFTHERESTAURANTASWELL,“THE31YEAROLDTELLSENJOYSHANGHAI“INHOTELS,FOREXAMPLE,THESEJOBSARESTRICTLYDEMARCATED,SOITSAGREATOPPORTUNITYTOLEARNHOWABUSINESSOPERATESACROSSTHEBOARD“ITWASATASKTHATMANAGEMENTBACKINSUNNYCALIFORNIAEVIDENTLYFELTHEWASREADYFOR,ANDAVOTEOFCONFIDENCEFROMACOMPANYTHAT,TODATE,HASOPENED250OUTLETSIN11COUNTRIESANDFORADDEDPRESSURE,THESHANGHAIBRANCHWASALSOCPKSCHINADEBUT“FORSUREITWASABIGSTEP,ANDUNLIKEALLTHEIROTHERASIAOPERATIONSTHATAREFRANCHISES,THEYDECIDEDTOMANAGEITDIRECTLYTOBEGINWITH,“SAYSSIMPSONTWOYEARSAGOAPRIVATEFRANCHISEETOOKOVERTHELEASE,BUTTHELINKSTOCPKHEADQUARTERSARESTILLSTRONG,WITHAMAINLANDBASEDBRANDAMBASSADORONHANDTOENSURETHEBUSINESSADHERESTOITSETHOSOFCREATING“INNOVATIVE,HEARTHBAKEDPIZZAS“,ASLICEOFPRBLURBTHATSIMPSONINSISTSLIVESUPTOTHEHYPE“THEYAREVERYINNOVATIVE,“HESAYS“THEPROBLEMWITHMOSTFASTFOODPLACESISTHATTHEYUSETHESAMESAUCEONEVERYPIZZAANDJUSTCHANGETHETOPPINGSEVERYONEOFOUR16PIZZASAUCESISAUNIQUERECIPETHATHASBEENFORMULATEDTOCOMPLEMENTTHETOPPINGSPERFECTLY“THELARGELYLOCALCUSTOMERBASEEVIDENTLYAGREESANDONSATURDAYANDSUNDAY,ATLEAST,THEPLACEISTEEMINGTHEKIDSEATFORFREEPOLICYATWEEKENDSISUNDOUBTEDLYABIGDRAW,ASWELLASISTHESPACIOUSSECONDFLOORLAYOUTOVERLOOKEDBYACANOPYOFGREENFROMFUXINGPARKOVERTHEROADTHECOMPANYISALSOFOCUSINGONINCREASINGBRANDRECOGNITIONANDINRECENTYEARSHASTAKENPARTINOUTSIDEEVENTSSUCHASTHEREGULARCALIFORNIAWEEKSTILL,THESTAAREHONESTENOUGHTOADMITTHATBUSINESSCOULDBEBETTERASGOOD,INFACT,ASINCPKSSECONDOUTLETINTHEPOPULARKERRYPARKSIDESHOPPINGMALLINPUDONG“SINANMANSIONSHASREALLYSTRUGGLEDTOGETTHENUMBEROFVISITORSTHATWEREENVISAGEDWHENITFIRSTOPENED,ANDITHASNTBEENEASYFORANYOFTHETENANTSHERE,“ADDSSIMPSON“WEREPLANNINGATHIRDOUTLETINTHECITYIN2015,ANDWEWILLPROBABLYCHOOSEASHOPPINGMALLAGAINBECAUSEOFTHEBETTERFOOTTRAFFIC“THETEAROOMSONCEFREQUENTEDBYCOCOCHANELANDMARCELPROUSTAREUPPINGSTICKSANDCOMINGTOSHANGHAI,XUJUNQIANVISITSTHEPARISIANOUTPOSTWITHSWEETTREATSONETHINGTHECENTURYOLDPARISIANTEAROOMANGELINAHASSHOWNISTHATLEGENDARYFASHIONDESIGNERCOCOCHANELNOTONLYHADSTYLEANDGLAMORBUTALSOBOASTEDGREATTASTEINFOOD,PASTRIESINPARTICULARONEOFTHEMOSTPOPULARTEAROOMSINPARIS,ANGELINAISFAMOUSFORHAVINGONCEBEENFREQUENTEDBYCELEBRITIESSUCHASCHANELANDWRITERMARCELPROUSTNOWANGELINAHASPACKEDUPITSFRENCHAMBIENCE,EFFICIENTSERVICE,ANDBEAUTIFUL,COMFORTINGDESSERTSANDFLOWNTHEMTOSHANGHAIATTHEFLAGSHIPDINEINANDTAKEOUTSPACEINSHANGHAI,EVERYTHINGMIMICSTHEORIGINALTEAROOMDESIGNEDFROMTHEBEGINNINGOFTHE20THCENTURY,INPARIS,THEHEIGHTOF“BELLEEPOQUE“THEPAINTINGSONTHEWALL,FOREXAMPLE,AREEXACTLYTHESAMEASTHEONETHATDEPICTSTHELANDSCAPEOFSOUTHERNFRANCE,THEHOMETOWNOFTHEOWNERANDTHESMALLTABLESAREINTENTIONALIMITATIONSOFTHEONESTHATCOCOCHANELONCESATATEVERYAFTERNOONFORHOTCHOCOLATETHEFAMOUSHOTCHOCOLATE,KNOWNASLAFRICAIN,ISALUXURIOUSMIXTUREOFFOURTYPESOFCOCOABEANSIMPORTEDFROMAFRICA,BLENDEDINPARISANDTHENSHIPPEDTOSHANGHAIITSSINFULLYSWEET,RICHANDTHICKASIFPUTTINGABAROFMELTINGCHOCOLATEDIRECTLYONTHETONGUEANDTHEFRESHWHIPPEDCREAMONTHESIDEMAKESALIGHT,BUTEQUALLYGRATIFYINGCONTRASTITISALSOSOLDINGLASSBOTTLESASTAKEAWAYTHESIGNATUREMONTBLANCCHESTNUTCAKECONSISTSOFTHREEPARTSTHEPUREEDCHESTNUTONTOP,THEVANILLACREAMLIKESTUFFING,ANDTHEMERINGUEASBASEGETALLTHREELAYERSINONESCOOP,NOTONLYFORTHEDIFFERENTTEXTURESBUTALSOVARIOUSFLAVORSOFSWEETNESSTHEDESSERTHASMAINTAINEDITSPOPULARITYFORACENTURY,EVENINACOUNTRYLIKEFRANCE,PERHAPSTHEWORLDSMOSTCOMPETITIVEPLACEFORDESSERTSAMUCHOVERLOOKEDPAIRING,ISTHEPARISNEWYORKCHOUXPASTRYANDN226CHOCOLATEFLAVOREDTEATHECHOUXPASTRYISAMOUTHFULOFAIRYPECANFLAVOREDWHIPPEDCREAM,WHILETHETEA,ABLENDOFBLACKTEASFROMCHINAANDCEYLON,COCOAANDROSEPETALS,OFFERSAMORESUBTLEFRAGRANCEOFFLOWERSANDCHOCOLATEORDERINGTHESETWOITEMS,FEATURINGAMUTEDSWEETNESS,MAKESITEASIERFORYOUTOFITINTOYOURLITTLEBLACKDRESSBREAKFAST,BRUNCH,LUNCHANDLIGHTSUPPERAREALSOSERVEDATTHETEAROOM,“AHUBOFMANYCULTURES“ANDTAKESIN“AMIXOFDIFFERENTSTYLESOFFRENCHCUISINES“,ACCORDINGTOTHEMANAGEMENTTEAMTHESEMICOOKEDFOIEGRASTERRINE,ISSEDUCTIVEANDDECEPTIVEITSGENEROUSLYSERVEDATTHESIZEANDSHAPEOFATOAST,WHILETHEACTUALBRIOCHETOASTISBAKEDINTOACURVEDSLICEDIPPEDWITHFIGCHUTNEYTHEFLAVOR,HOWEVER,ISHONESTSTRONG,SMOOTHANDSUBLIMEANDYOUDONTACTUALLYNEEDTHETOASTFORCRUNCHINESSTHISISTHESEASONFORHIGHTEAS,WITHDAINTYCUPSOFFINECHINAANDLITTLEPASTRIESTHATAPPEALTOBOTHVISUALANDPHYSICALAPPETITESBUTTHEREISONEHIGHTEAWITHADIFFERENCE,ANDPAULINEDLOHFINDSOUTJUSTEXACTLYWHYITISSPECIALEARLGREYTEAANDMACARONSAREALLVERYWELLFORTHECRUCIALRECUPERATIVEBREAKINBETWEENINTENSIVEBOUTSOFHOLIDAYSEASONSHOPPINGANDFORTHOSEWHOPREFERSAVORYTOSWEET,THEREISSTILLTHESELECTIONOFCLASSICCHINESESNACKSCALLEDDIMSUMTOSATISFYANDSATIATEHIGHTEAISAMEALTOEATWITHEYEANDMOUTH,ANINBETWEENINDULGENCETHATSHOULDBELIGHTENOUGHNOTTOSPOILDINNER,BUTSUFFICIENTLYROBUSTTOTAKETHEEDGEOFFTHEHUNGERTHATSTRIKESHOURSAFTERLUNCHTHEAFTERNOONTEASPECIALATSHANGXIATTHEFOURSEASONSHOTELPUDONGHASJUSTTHERIGHTELEMENTSITISAPAMPERINGMEAL,WITHTOUCHESOFLUXURYTHATMAKETHEHIGHTEASESSIONATREATINITSELFWHOLEBABYABALONESAREBRAISEDANDTHENTOPPEDONASHORTCRUSTPASTRYSHELL,ASORTOFCHINESEVERSIONOFTHEWESTERNVOLAUVENT,BUTCLASSIEREVENCLASSIERISTHEDIMSUMSTAPLESHRIMPDUMPLINGORHARGOW,UPGRADEDWITHTHEADDITIONOFSLIVERSOFMIDNIGHTDARKTRUFFLESTHISISAMASTERTOUCH,ANDCHEFSIMONCHOI,WHOPRESIDESUNCHALLENGEDATSHANGXI,HASSCOREDAWINNERAGAINSWEETPRAWNSANDAROMATICTRUFFLESWHATSNOTTOLOVEHISMASTERFULCRAFTSMANSHIPISEXHIBITEDINYETANOTHERPASTRYASWEETPASTRYTHATISSHAPEDTOLOOKLIKEAWALNUT,BUTWHICHYOUCANPUTSTRAIGHTINTOTHEMOUTHITCRUMBLESIMMEDIATELY,ANDTHESLIGHTLYSWEET,NUTTYMORSELISSOEASYTOEATYOULLPROBABLYREACHSTRAIGHTFORANOTHERMYFAVORITEISTHEDESSERTTHATGOESBYTHENAMEYANGZHIGANLU,ORAMBROSIAFROMTHEGODSTHEHOTELCALLSITCHILLEDMANGOCREAMWITHSAGO,POMELOANDBIRDSNESTMADEWITHINGREDIENTSTHATRESONATEWITHEVERYFEMALESOULITDOESTASTELIKEAMBROSIA,WITHTHESWEETSOURFRAGRANCEOFTHEMANGOFORMINGTHEFIRSTLAYEROFTASTEANDSENSATION,ANDTHEPOMELOSACSANDSAGOPEARLSPROVIDINGTHETACTILECONTRASTTHEBIRDSNESTITSTHEINGREDIENTTHATGILDSTHE