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Solved: /11 Exercises 99-106, use the formula ill Exercise

Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence ISBN: 9780131871410 187

Solution for problem 104 Chapter 6.1

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

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Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

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Problem 104

/11 Exercises 99-106, use the formula ill Exercise 98to detennine the a11gle betwee11 the vectors u a11d v. 104. u = [-!] and v = [ ~]

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PSY 311 Emotion Chapter 14 Emotion on Cognition & Memory Emo▯ons&Learning • Yerkes-DodsonLa:w ◦ Learningisbestdonewhens▯mula▯on/arousalisn'ttostrongorweak ◦ Learning,memory,performance,&reasoningaremostenhancedundermediumlevels ofarousal/mo▯va▯on/emo▯on Emo▯on&A▯en▯on • Studyona▯en▯on: ◦ Computerscreendisplayspairsof1-digitnumbersseparatedbyaword ◦ I.E."5chart8" ◦ Taskistopress1keyifbothnumbersareoddoreven,orotherkeyifthereisa combina▯onofodd&evennumbers&ignorethewordinbetween ◦ Emo▯onalwordssuchas"kill"arehardertoignore&par▯cipantstakelongertopress keys ◦ Emo▯onalwordsdistracta▯en▯on&slowpar▯cipants'responsesmorethanneutral wordsdo • Fearfocusesone'sa▯en▯on&decreasesa▯en▯ontoothers▯muli • Picturesofangryfacesa▯ract&holdmorea▯en▯on&evokemorecor▯calarusalthanpictures ofhappyorneutralfaces(Schupp2004) • Ac▯velythreateningpicturescapturea▯en▯onevenifpresentedinperipheralvision ◦ Ifaspecificpicturehasbeencondi▯onedw/aloudnoise,theviewerimmediately a▯endstothepictureevenifit'sfarofftotheside(Kosteretal.2004) • Pplpronetostronganxie▯esespeciallylikelytolookawayfromdistressingpictures(Calvo2005) ◦ Threatenings▯mulicapturea▯en▯onquickly,butpplthentrytoavoidit • Broaden&BuildTheory: ◦ Posi▯veemo▯onsshouldexpandourfocusofa▯en▯on&see"thebigpicture" ◦ Par▯cipantsinaposi▯vemoodaremorecrea▯ve&a▯endmoretotheglobal characteris▯csofcomplexfigures • Posi▯veemo▯ons: ◦ Donotallinvolveapproachmo▯va▯ontothesamedegree ◦ Strongapproachmo▯va▯on/rewardseekingnarrowsa▯en▯on&leadstofocusonlocal details • Gable&Harmon-Jones2008: : spuo r g 2 deng i s◦sA • Watchedshortfilmclipw/cats • Watchedcliponyummydesserts ◦ Allpar▯cipantscompletedglobal-locala▯en▯ontaska▯er • Par▯cipantswhowatchedcatschosefiguresonthebasisofglobalsimilarity • Par▯cipantswhowatcheddessertsbasedjudgmentsmoreondetails ◦ Emo▯onona▯en▯ondoesn'tjustdependonvalenceofemo▯on,butspecificemo▯on& func▯ons • Par▯cipantstendtospendmore▯melookingatpleasantimagesthanneutralones PSY 311 Emotion Emo▯ons&Memory • Wea▯endmoretoemo▯onallypowerfuls▯muli&aremorelikelytorememberthem • Concentra▯onGame(Adolphsetal.2001): ◦ Whenpar▯cipantslookatunemo▯onalpictures,theyremembercombina▯onofcentral objects&backgrounddetails • Asifunemo▯onalsceneswereviewedfromafurtherdistance ◦ Fordistressingpictures,centralobjectsarerememberedwell,&backgrounddetailsare forgo▯en • Asifemo▯onalsceneswereviewedfromacloserperspec▯ve • Emo▯onalarousalfacilitatesmemory(Schmidt2002): ◦ Par▯cipantslookedatphotographsofppl&reportedlaterwhattheyrememberedof them ◦ Par▯cipantsmostlyrememberedthesolenudephotoverywell • Rememberedalmostnothingaboutthebackgrounddetailsornext2or3 picturesfollowingthenude • Memorycanbedetachedfroma▯en▯on(Ackerman2009): ◦ Par▯cipantsplayedconcentra▯ononthecomputer,matchedpairsofphotoswhile viewingonly1photoata▯me ◦ Mixedsetofdistorted&regularpicturesoffaces ◦ Par▯cipantspaidmorea▯en▯ontodisfiguredfaces ◦ Mademoremistakestryingtomatchthedisfiguredones ◦ Memoryisenhancedbya▯en▯onbutisaffectedbyotherfactorsaswell Emo▯on&MemoryForma▯on • Emo▯onenhancesforma▯on&intensityofmemories • Heightenedemo▯onsstrengthenthememoriesformedduringevents,buteffectbreaksdown atextremelevelsofemo▯on • Bradley1992: ◦ Par▯cipantsviewed60photosofobjects&events ◦ Rangedfromeverydayobjectstoextremesportsorgorypictures ◦ Par▯cipantsthenratedphotosaccordingtohowcalmorarousedtheymadethemfeel& howpleasant/unpleasanttheywere ◦ Par▯cipantsthenaskedtobrieflydescribeasmanypicturesaspossible ◦ Morelikelytorememberstronglyarousingpictures ◦ S▯llmorelikelytorememberintense/arousal-producingphotosayearlater • Pplrememberemo▯onallychargedpicturesbe▯erthanneutralonesevenwhenpresented rapidly&w/divideda▯en▯on ◦ Resultssimilarw/wordmemory ◦ Rememberedemo▯onally-chargedwordsbe▯erthanneutralwords&remembered themmorevividly Hormones • Emo▯onalarousalincreasesreleaseofepinephrine(adrenalin)&cor▯solfromadrenalgland ◦ S▯mulatevagusnerve->exciteamygdala • Directinjec▯onsofepinephrineorcor▯solstrengthenmemoryofeventsjustexperienced • Directs▯mula▯onofvagusnerveoramygdalainlabanimalsstrengthensmemorystorage • Mildstressthatdoesn'tlasttoolonghelpsinforma▯onofmemories PSY 311 Emotion • Weakenedphysiologicalarousalweakensmemorystorage: ◦ 2par▯cipantgroups: 1. Tookbeta-blockerpills(disablessympathe▯carousal) 2. Tookplacebo ◦ Par▯cipantsthenviewedslideshowofwreckedcars,anemergencyroom,brainscan,& surgery ◦ 2versionsofthestory: 1. Neutralversion-boywalksbyjunkyardtolookatcars,visitsdad'sworkatthe hospital,watchessurgicalteamprac▯ce 2. Arousalversion-boyishitbyacar,rushedtothehospital,brainscanshows brainbleeding,needssurgery ◦ 1weeklaterpar▯cipantsanswered80mul▯plechoiceques▯onsaboutslides&stories • Par▯cipantshearingtheneutralversionhadmediocrescores(answered2/3rds correctly) • Par▯cipantsinarousalversion: ▪ Beta-blockerpill-performedthesameasneutralpar▯cipants ▪ Placebo-answeredabout85%correctly • fMRIshowsamygdalaismoreac▯vewhenviewingemo▯onallyintenseslides ◦ Thegreaterdegreeofamygdalaac▯vity,themoreaccuratelytheimagesare remembered ◦ Amygdala-damagedppldon'trememberemo▯onalelementsaswellasothersdo Emo▯on&MemoryStorage • Flashbulbmemories-Vivid,highlydetailedmemoriesw/photographicquality ◦ Feeldetailed&life-like ◦ I.E.rememberingthe▯me&placewhereyouwerewhen9/11happened ◦ Nomoreaccurateoverlongtermthanmundanememories ◦ ResearchersaskedUSstudentstorecalldetailsofwhattheyweredoingwhentheyfirst heardabout9/11 ◦ Memorieschanged/becamelessaccuratewhenrepor▯ngmonthslater • Par▯cipantsviewingneutral&unpleasantphotosrememberbothequallywell,butfeelmore confidentrememberingunpleasantphotos • MacKay2005: ◦ Studentsobservedcoloredwordsdisplayedalloveracomputerscreen ◦ Taskwastoignorewords&saycoloroftheink ◦ Halfthewordswerenamesofanimals,otherhalfprofani▯es/insults ◦ Wordsappearedrepeatedlyinthesameloca▯ons ◦ Studentsaskedtoiden▯fyloca▯onsofrepeatedwordsrememberedexplicitwordsmore accuratelythanneutralones • Eyewitnessreportsincourto▯eninaccurate&confidencenothighlycorrelatedw/memory accuracy Emo▯on&MemoryRetrieval • Emo▯onalexperiences: ◦ Studentsonaspringbreaktripweregivingdevicesbeepingat7random▯mesaday ◦ Studentsreportedemo▯onsatthemomentofthebeep PSY 311 Emotion ◦ Filledoutaques▯onnairea▯erreturningfromtripabouthowmuchtheyenjoyedit ◦ Onavg,reportedpleasantnessofthetripsubstan▯allygreaterthanavgreportsduring thetrip ◦ Ourmemoryofanexperienceisnotanavgofemo▯onsoverthewhole▯mebuta reflec▯onofsomehighlights • Currentemo▯onsmodifywhateventsweremember ◦ Werememberhappyeventswhenwe'reinagoodmood&viceversa ◦ Consistentw/fright&angeraswell Emo▯on&Informa▯onProcessing • Situa▯onexperiment: ◦ Par▯cipantswarmedupbysadness-producingoranger-producingexercises ◦ Toldtoimaginethemselvesinanawkwardrejec▯onsitua▯on ◦ Angrypar▯cipantsmorelikelytoblameppl,sadpar▯cipantsmorelikelytoblame circumstances/luck • Par▯cipantswri▯ngessays: ◦ 1grouptoldtowriteabouthowa▯acksmadethemangry ◦ 2ndgroupwroteabouta▯acksmakingthemsad ◦ 3rdgroupwroteabouta▯acksmakingthemafraid ◦ Par▯cipantsthenaskedhowmuchdangertheyforeseeforthemselves&theUSinthe nextyear ◦ Par▯cipantswri▯ngaboutfeares▯matedgreaterprobabili▯esofdangerforthemselves &US • Emo▯onsinfluencehowweinterpret&reasonaboutsitua▯ons,whatwea▯endto,&whatwe rememberaboutthem AffectValence&Systema▯cvs.Heuris▯cProcessing • Systema▯ccogni▯on-thorough&deliberateanalysisofavailableinforma▯on • Heuris▯ccogni▯on-makingdecisionsonthebasisof"ruleofthumb"orpersonalexperiences • Centralroutetopersuasion-providingfacts&logic ◦ Pplrespondbe▯eriftheyfeeltheirdecisionshavemajorconsequences&areworththe effort • Peripheralroutetopersuasion-superficialfactorssuchasrepea▯ngslogansorendorsements bycelebri▯es ◦ Pplstar▯ngasambivalenttopersuasivemessagesarelesslikelytoques▯onthesource ofthemessage ◦ Happymoodmakespplmoresuscep▯bletoperipheralrouteinfluences&less suscep▯bletocentralroute • Moreapttojumptoconclusionsw/oexaminingevidence ◦ Sadpplpaymorea▯en▯ontoqualityofevidence • Bless1990: ◦ Studentsrandomlyassignedtowriteabouthappyorsadeventstoinducehappyorad mood ◦ Thenlistenedtoeitherstrong/factualargumentsorweak/superficialargumentsabout raisingstudentfeesattheiruniversity ◦ Studentsinahappymoodequallypersuadedbystrong/weakarguments PSY 311 Emotion ◦ Sadstudentspersuadedjustbythestrongargument ◦ Sadmoodtendstopromotemorecarefulanalysisofarguments • Happypplmorelikelytoapplystereotypes&explainbehaviorsintermsofpersonalitytraits ratherthansitua▯onalfactors ◦ Alsotendtorelyonscripts&schemasduringrecallthanactualfacts/eventsthattook place • Sadnessdiscouragesrelianceonstereotypeswhenjudgingnewtargets Posi▯veAffect&Crea▯vity • Posi▯veaffecthassomecogni▯veadvantages ◦ Candleexperiment-par▯cipantsinahappy/amusedmoodmorelikelytosolveproblems crea▯vely&faster • Depressiverealism-Pplwhoaremildlydepressedaremorerealis▯cthanhappy/op▯mis▯cppl ◦ Morelikelytoperceivethemselves&situa▯onsaccurately ◦ Makemorecareful/correctdecisions • Perceivingcontrol: ◦ Par▯cipantstoldtocontrolfrequencyofagreenlightappearing ◦ Inse▯ngswherepar▯cipantshadnocontrol: • Non-depressedstudentses▯matedhaving40%control • Dysthymic(depressed)studentses▯mated15%control,recognizedlack • Predic▯onstudy: ◦ Dysthymicstudentsslightlymoreaccurateatpredic▯ngfuturesadevents,suchascrying ◦ Happierstudentsmoreaccurateatpredic▯ngfuturepleasantevents,likehowo▯enthey wouldlaugh • Self-appraisal ◦ 2setsofstudentsgiventhesame,neutral"personalityreport" ◦ Dysthymicstudentsratedprofilesasunfavorable ◦ Otherstudentsratedthemasfavorable ◦ Dysthymiarevealedbiastoseeone'sselfinanega▯velight Emo▯ons&DecisionMaking • AffectInfusionModel ◦ Peopleusetheircurrentemo▯onalstateasinforma▯oninreachingadecisionabout sometarget ◦ Evenifthetargetdidnotevoketheemo▯on ◦ I.E.Peoplearemorelikelytoanswerposi▯velywhenaskedhowthey'redoingona sunnydayvs.arainyday • Thoughthe"cloudyday"effectdisappearsiftheweatherisexplicitlybroughtto par▯cipants'a▯en▯on • Posterstudy: ◦ Par▯cipantsinvitedtolookatposters&takeonehome ◦ 1groupinstructedtowritedownreasonsforchoosingtheirmajor ◦ Othergroupinstructedtowritethingstheylikedordislikedabouteachposter • Reasonsmanipula▯on ◦ Allpar▯cipantsratedhowmuchtheylikedeachposter PSY 311 Emotion ◦ Par▯cipantsin"reasons"manipula▯onlessdiscrimina▯nginra▯nga▯rac▯venessof posters • Morelikelytotakeafunnyposterhomeratherthananartprint : r e t a l s keew◦3 • Par▯cipantswhocarefullylistedreasonsforliking/dislikingeachposterwereless sa▯sfiedw/theirchoice Emo▯ons&MoralReasoning • TrolleyDilemma: ◦ Atrolleycar'sbrakesfail&isheadingtoward5pplwhocan'tescape ◦ Par▯cipantstoldtheyhaveaswitchthatcontrolswhichtrackthetrolleycantake ◦ 1trackkills5ppl,theothertrackkills1 ◦ Otherop▯onistopushawrestlerinfrontofthetrolleytosavethepplbutkillhim • Foundthatpar▯cipantsfeltusingphysicalforcetodirectlyharmsomeonefeelsimmoral,while incidentalharmresul▯ngfromourmanipula▯onfeelslessproblema▯c Limita▯onsofRelyingonEmo▯ons • Whenmakingdecisionsbasedonliking&preference: ◦ Subconscious/affec▯veprocessingmayleadtoabe▯erdecisionthansystema▯canalysis • Pplacrosscountriestendtopreferbetsw/averysmallchanceofaveryhighrewardratherthan ahighprobabilityofaverylowreward ◦ Duetoan▯cipa▯ngpleasure

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Chapter 6.1, Problem 104 is Solved
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Textbook: Elementary Linear Algebra: A Matrix Approach
Edition: 2
Author: Lawrence E. Spence
ISBN: 9780131871410

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Solved: /11 Exercises 99-106, use the formula ill Exercise