3.4.1TheDefinitionofVectorSpaceLinearAlgebraDefinition(VectorSpace)Avectorsetiscalledavectorspaceifithas𝑉thefollowingthreeproperties.Vectorsetisnotempty𝑉(closedundervectoraddition)Ifandbelongto,belongstoV𝑉(closedundervectoraddition)Ifbelongstoandisascalar,belongstoV𝑉2)Thedefinitionalsospecifiesstepstoverifywhetheravectorsetisavectorspace:①Visnotempty;②Visclosedundervectoraddition;③...
LinearAlgebra3.3.3CalculationofthelargestIndependentgroupandRankofVectorGroupsExampleCalculatetherankandalargestindependentgroupofthefollowingvectorgroup:Solution:Method1Discriminatingthecorrelationofvectorgroups.𝛼3=𝛼1+2𝛼2.arelinearlydependentandarelinearlyindependent.𝛼1=(32−1−3−2),Thus,therankofthevectorgroupis2,andisalargestindependentgroupTheorem8TherankofmatrixAisequaltotherankofther...
LinearAlgebra3.3.2PropertiesoftheLargestIndependentGroupsandRankQuestion3.Ifthevectorgroupitselfislinearlyindependent,whatisthelargestindependentgroupofthevectorgroup?Property1.AvectorgroupislinearindependentThenumberofvectorsitcontainsisequaltoitsrank.1=1002=,0103=001Conclusion1.I0:1,2,,rislinearlyindependent,thenthelargestindependentgroupofI0isitself.Forexample,in11,01,10,3=1=...
LinearAlgebra3.3.1DefinitionofTheLargestIndependentGroupandRankofVectorGroupsR:255G:255B:0R:255G:0B:255R:0G:255B:2552550RedGreenBlue002552550002550Thepracticalmeaningofn-dimensionalvectorswhereVisiblecolorsinnaturecanbeobtainedbymixingprimarycolorswithcertainproportions,thatis,anycolorisregardedasalinearcombinationofred,greenandbluecolorvectors.Theprimarycolorsshouldbeindependenttoeachother,tha...
LinearAlgebra3.2.2PropertiesofLinearCorrelationofVectorGroupsTheorem6VectorgroupA:islinearlydependent,ÛTherankofthematrixA=()<m(thenumberofvectors).VectorgroupA:islinearlyindependent,ÛTherankofthematrixA=()=m(thenumberofvectors).Note:1)Theconclusionalsoholdsfortherowvectorcase.ExampleDeterminethelinearcorrelationofvectorgroupSolution:LetObviously,usingTheorem6todeterminethecorrelationisverysi...
LinearAlgebra3.2.2PropertiesofLinearCorrelationofVectorGroupsTheorem1VectorgroupA:islinearlydependentThereisatleastoneofthevectorsisalinearcombinationofother−1vectors.𝑚Proof(Sufficiency)Givenavectorin(suchas)thatcanbelinearlyrepresentedbytheremainingvectors,so𝛼𝑚=𝜆1𝛼1+𝜆2𝛼2+⋯+𝜆𝑚−1𝛼𝑚−1⇒𝜆1𝛼1+𝜆2𝛼2+⋯+𝜆𝑚−1𝛼𝑚−1+(−1)𝛼𝑚=𝑂Obviouslyarenotallzero,soislinearlydependent.Thatis...
LinearAlgebra3.2.1DefinitionofLinearDependentofVectorGroupsandarecollinearGeometry:Thereisauniquerealscalark,suchthat=kTherearerealscalarssuchthat.Geometry:𝑘2¿𝑘1+𝑘2andarenotcollinear;and,arecoplanar.TherearerealscalarssuchthatTherearerealscalarssuchthatDefinitionVectorgroupislinearlydependent,iftherearescalarsthatarenotallzero,suchthatOtherwise,itisca...
TransformationofAgrobacteriumThawthecompetentAgrobacteriumoniceandadd2gDNA,mix(notvertex)Incubate5minoniceFreezeinliquidnitrogenfor5minIncubateat37oCfor5minAddedthe1mlprewarmed(28oC)YEPmediumShakefor2–4hoursat28oCPlate5x200µlaliquitsonYEPPlate(withrifandkan)Incubateplateat28oCforca2days.(normallyyouwillget250cfu/µgifplasmidqualityisgood)--------YEPplate500mlYEPmedium+500µlRif(50mg/ml)+500µlkann(50µmg{ml)
DifferentialGeometryofCurvesandSurfacesManfredoP.doCarmoInstitutodeMatematicaPuraeAplicada(IMPA)RiodeJaneiro,BrazilPrentice-Hall,Inc.,UpperSaddleRiver,NewJersey07458ContentsPrefacevSomeRemarksonUsingthisBookvii1.Curves11-1Introduction11-2ParametrizedCurves21-3RegularCurves;ArcLength51-4TheVectorProductinR3//1-5TheLocalTheoryofCurvesParametrizedbyArcLength161-6TheLocalCanonicalForm271-7GlobalPro...
TheEffectsofGroupCounselingandSelf-AffirmationonStigmaandGroupRelationshipDevelopment:AReplicationandExtensionAndrewJ.Seidman1,NathanielG.Wade2,andJasonGeller31DepartmentofPsychiatry,UniversityofPittsburgh2DepartmentofPsychology,IowaStateUniversity3CenterforCognitiveScience,RutgersUniversityThestigmaofseekingcounselingandnegativeattitudesaboutcounselingareprimarybarrierstoitsuse.Intheonlyknowns...
BRIEFREPORTPreventionofAnxietyandDepressioninSchoolChildren:EffectivenessoftheTransdiagnosticEMOTIONProgramKristinD.MartinsenUniversityofOsloandCentreforChildandAdolescentMentalHealth,EasternandSouthernNorway,Oslo,NorwayLeneMariP.RasmussenTheRegionalCentreforChildandYouthMentalHealthandChildWelfare–North,Tromsø,NorwayToreWentzel-LarsenandSolveigHolenCentreforChildandAdolescentMentalHealth,Eas...
ResearchArticleInterventionEffectofGroupCounselingBasedonPositivePsychologyonPsychologicalCrisisofCollegeStudentZixiZhang,1YaboLi,1SailanSun,1andZiyeTang21QiannanNormalCollegeforNationalities,Duyun,China2QiannanNationalityProfessionalTechnologyCollege,Qiannan,ChinaCorrespondenceshouldbeaddressedtoZiyeTang;ziyetang66@163.comReceived16March2022;Revised15May2022;Accepted25May2022;Published12August...
AnExperimentalExaminationofTwoCareerInterventionsforBatteredWomenKristaM.ChronisterandEllenHawleyMcWhirterUniversityofOregonTheauthorstestedtheeffectivenessof2groupcareerinterventionsfor73batteredwomenwhowererandomlyassignedto1of2treatmentconditionsorawait-listcontrolgroup.Bothinterventionsincludedthe5mosteffectivecareerinterventioncomponentsidentifiedbyS.D.BrownandN.E.Krane(2000),and1oftheinte...
Module6UnexplainedMysteriesoftheNaturalWorldTheStonehengeStonehenge,themostfamousprehistoricmonumentinBritain,issituatedonSalisburyPlaininthecountyofWiltshire.AtvarioustimesregardedasasitebuiltbytheDruids,theRomans,theDanesandeventheFrench,thefirststage—acircularditchandbankwithanentranceflanked1byapairofsmallstandingstones—isbelievedtohavebeenbuiltaround3000BC.Thesitewasabandonedlaterandrebu...
SectionⅢIntegratingSkills一二三一、根据词性及汉语提示写出相关单词1.destructionn.毁坏→(反义词)2.generousadj.慷慨的→n.慷慨3.unpredictableadj.变幻莫测的→(反义词)→v.预测4.emperorn.皇帝→n.女皇,皇后5.positiveadj.正面的→(反义词)6.indicatev.象征,暗示→n.暗示7.fortunen.运气,命运,财富→adj.幸运的→adj.不幸的8.identityn.身份,特性→vt.辨别答案:1.construction2.generosity3.predictable;predict4.empress...
SectionⅣWriting写作指导常用句式针对训练如何描写自然之谜写自然之谜类的文章,要有科学依据,不能凭空杜撰,选材必须来自科学文献或权威机构。可按如下写作步骤进行写作:首先,简单介绍怪异事件及其发生的地点;其次,详细叙述怪异事件或描述怪物的特征;最后,试着解开谜团。自然界有很多未解之谜,这些神秘的现象激励着科学家们不懈地探索。对于自然传说的介绍要注意:1.文章通常由三大段落组成。首先交代清楚传说的内容。然后详细介...
SectionⅡGrammar一二三四一、阅读课文,找出与下列汉语意义相匹配的英语句子1.许多人认为,天池里的怪物或许是苏格兰尼斯湖怪物的远房表亲。2.他们还认为,在世界其他地方的湖泊中可能也有类似的怪物。3.他们说,水温这样低的湖泊不可能生存有体形如此巨大的动物。一二三四二、核对答案,并对这几个句子进行逐一剖析1.ManypeoplethinkthemonstermaybeadistantcousinoftheLochNessmonsterinScotland.2.Theyalsothinkthattheremightbe...
Module1Wondersoftheworld讲义（含解析）外研版九年级英语上册Module1Wondersoftheworld一、词汇学习Unit1Itsmellsdelicious.序号例句和生词图片单词和音标词性和中文意思笔记1Thisparkhasaman-madelake.man-made/mnmed/adj.人造的2Onlythenaturalvegetablesarehealthynatural/ntrl/adj.大自然的3TheGreatWallisoneofthewondersoftheancientworld.wonder/wnd/n.奇观，奇迹Hesstartingtowonderwhetherhedidtherightthinginaccept...
Unit14IremembermeetingallofyouinGrade7单元作业设计（含核心素养目标，5课时）人教版英语九年级全册Unit14IremembermeetingallofyouinGrade7.作业单元设计一、单元信息基本信息学科年级学期教材版本单元名称英语九年级第二学期人教版Unit14IremembermeetingallofyouinGrade7.单元组织方式自然单元□重组单元课时信息序号教学内容课型课时1SectionA1a-2d听说第1课时2SectionA3a-4b读写第2课时3SectionB1a-1e听说第3课时4Sectio...
Unit10ProfitsofPraiseArewetooquicktoblameandslowtopraise?Itseemsweare.ItwastheendofmyexhaustingfirstdayaswaitressinabusyNewYorkrestaurant.Mycaphadgoneawry,myapronwasstained,myfeetached.TheloadedtraysIcarriedfeltheavierandheavier.Wearyanddiscouraged,Ididntseemabletodoanythingright.AsImadeoutacomplicatedcheckforafamilywithseveralchildrenwhohadchangedtheirice-creamorderadozentimes,Iwasreadytoquit....
