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Midterm

MAT224 MIDTERM SELF GENERATED SOLUTION 2009 PART2.pdf

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Department
Mathematics
Course
MAT224H1
Professor
All Professors
Semester
Winter

Description
UniversityofTorontoDepartmentofMathematicsMAT224H1FLinearAlgebraIIMidtermExaminationOctober222009SUppalDuration1hour50minutesLastNameGivenNameStudentNumberTutorialCodeNocalculatorsorotheraidsareallowedFORMARKERUSEONLYQuestionMark1525310410510610710TOTAL601of1151LetVbethesetoforderedpairsxyofrealnumberswiththeoperationsofvectoradditionandscalarmultiplicationgivenby0000xyxyxxyycxycxyIsVavectorspaceoverRwithrespecttotheseoperationsJustifyyouranswerSolutionCheckingthelistofpropertiesthatavectorspacemustsatisfyviaproperty3wendthattheadditiveidentityis01sinceforallab2Vwehaveab01a0b1abThenwecheckproperty4forallab2Vandwendthatifb60a1bisaninversesinceaba1baabb01Butifb0wemuststillhaveaninversesotheremustbesomecd2Vsuchthatcd0001butthissaysthatc0d001whichisimpossibletosolveThusthisisnotavectorspace2of11
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