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Midterm

MAT224 MIDTERM SELF GENERATED SOLUTION 2008.pdf

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Department
Mathematics
Course
MAT224H1
Professor
All Professors
Semester
Winter

Description
ForeachofthestatementsbelowdecideifitistrueorfalseIndicateyouranswerbyshadingintheboxcorrespondingtoyourchoiceJustifyyouranswerbyprovidinganappropriateprooforcounterexample41aTheadditiveinversevofavectorvinavectorspaceisuniquetruefalseLetvandvbetwoadditveinversesforvThenononehandsincevisanadditive121inverseforvvvvvvv0vv121222Ontheotherhandsincevisanadditiveinverseforv2vvvvvvvvv0vv12212111Thisgivesvvandtheadditiveinverseisunique1241bLetfbeanisomorphismfromavectorspaceVtoavectorspaceWIffv0thentruefalsev0IffisanisomorphismthenitisaonetooneontolineartransformationSincefisalineartransformationitmaps0to0Therforeifffv0thenv0sinceVWWVfisonetoone2of8
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