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Textbook Notes at University of Toronto St. George (page 3)

MAT223H1 Chapter Notes - Chapter 4.1: Scalar Multiplication, Mull, Root Mean Square
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IntroductiontoSubspaces n Subspacesarespecialsubsetsofavectorspace(Rinoursuchthat n X case)thatareconnectedtospanningsets,lineartransfor v=0: l mations,andsystemsoflinearequations. l=1 n Then,SisasubspaceofR. 1Subspaces 2H...

Mathematics
MAT223H1
Fabian Parsch
MAT223H1 Chapter Notes - Chapter 3.1: Codomain
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LinearTransformations Lineartransformationsareaspecialtypeoffunctionthat(a)ThevectorwisintherangeofTifandonlyifAx=wisa appearsinmanypracticaleldssuchasnance,engineerconsistentlinearsystem(ithasasolution). ing,socialscience...

Mathematics
MAT223H1
Fabian Parsch
MAT223H1 Chapter Notes - Chapter 3.3: Asteroid Family, Augmented Matrix, Block Matrix
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Inverses InthissectionweconsidertheproblemofreversingaTheorem1isquiteimportantbecauseitsaysthatifT: nn1n lineartransformation.R!Risaninvertibletransformation,thenT:R! n Risalsoalineartransformation. Hence,thereexistmatrice...

Mathematics
MAT223H1
Fabian Parsch
MAT223H1 Chapter Notes - Chapter 3.2: Matrix Addition, Diagonal Matrix, Block Matrix
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MatrixAlgebra Inthissectionwestudythealgebraofmatrices,thatisthe 2MatrixMultiplication arithmeticoperationsthatcanbeperformedovermatri cesandtheirproperties. Def.2(MatricesProduct). LetAbeannkmatrixandBakmmatrix.Thenthe Al...

Mathematics
MAT223H1
Fabian Parsch
MAT223H1 Chapter Notes - Chapter 4.2: Vandermonde Matrix
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BasisandDimension 2FindingaBasis 1BasisofaSpace n Thm.2. ConsiderthesubspaceofRdenedby LetAandBbeequivalentmatrices.Thenthesubspacespanned bytherowsofAisthesameasthesubspacespannedbytherows S=spanu;u;:::;u 12m ofB. Bydenit...

Mathematics
MAT223H1
Fabian Parsch
MAT223H1 Chapter Notes - Chapter 4.3: Bmw 8 Series, Row And Column Spaces
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RowandColumnSpaces Thm.2. 1RowandColumnSpaces ForanymatrixA,thedimensionoftherowspaceequalsthe dimensionofthecolumnspace. ConsideramatrixofnmdenedonR: 23 Def.2(RankofaMatrix). aaa:::a 1112131n TherankofamatrixAisthedimensi...

Mathematics
MAT223H1
Fabian Parsch
MAT223H1 Chapter Notes - Chapter 3.4: Asteroid Family, Diagonal Matrix, The Algorithm
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LUFactorization WewillnowrevisittheproblemofndingthesolutionstoImportantobservations: asystemoflinearequations. NotethatthetheoremdoesnotrequireAtobea LetAbeannmmatrixwithgeneralform squarematrix. 23 aa:::a Therecanbemoret...

Mathematics
MAT223H1
Fabian Parsch
MAT188H1 Chapter 2.2: Chapter 2.2 Span
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Span1SpanofaSetofVectorsThespanofasetofvectorsfu;u;:::;ugisasubsetof12mvectorspacedenedbyallpossiblelinearcombinationsofvectorsfromthatset.Def.1(SpanofSetofVectors).nLetfu;u;:::;ugbevectorsinR.Thespanofthissetis12mdenotedb...

Mathematics
MAT223H1
Fabian Parsch
MAT188H1 Chapter 2.3: Chapter 2.3 Linear Independence
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LinearIndependence1LinearIndependenceDef.1(LinearIndependence).nLetfu;:::;ugbeasetofvectorsinR.1mIftheonlysolutiontothevectorequationxu+xu+:::+xu=0(1)1122mmisthetrivialsolutionx=x=:::x=0;12mthenthesetForthecaseofsetswithth...

Mathematics
MAT223H1
Fabian Parsch
MAT223H1 Chapter Notes - Chapter 2.1: Commutative Property, Additive Inverse, Euclidean Space
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VectorsAddition:1Introduction232323u+vvu1111676767LinearAlgebraisthestudyofarithmeticoperationsperu+vvu2222676767=+u+v=676767...formedonvectors....454545...Inverysimpleterms,avectorisanorderedlistofnumu+vvunnnnbers,whichar...

Mathematics
MAT223H1
Fabian Parsch
MAT223H1 Chapter Notes - Chapter 1.1: The Algorithm
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LinesandLinearEquationsnosolutionisinconsistent.1IntroductiontoLinearEquationsWhatkindofsystemsarenaturallyinconsistent?TryingtoManyproblemsfromreallifeintechnology,socialscisolveences,andmanyotherhumanendeavorsrequiresolv...

Mathematics
MAT223H1
Fabian Parsch
MAT223H1 Chapter Notes - Chapter 1.2: Row Echelon Form, The Algorithm, Elementary Matrix
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LinearSystemsandMatricesisequivalentto1LinearSystemsElementaryOperationsax+:::+ax=b1111nn1...ax+:::+ax=bi11inni.Wepresentasystematicapproachforconvertinganylin.(3).earsystemintoitsechelonform.Thatisbasedontheuse(a+ca)x+:::...

Mathematics
MAT223H1
Fabian Parsch
MAT223H1 Chapter Notes - Chapter 1.3: Roundoff, Pivot Element, Golu
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NumericalSolutionsItworksonlyinsystemswithequalnumberofequa1Introductiontionsandvariables.Eliminationmethodsworkneforsmallsystems,butcanItssolutioncandiverge,meaningthatthesolutionleadtoerrorswhenimplementedoncomputersyste...

Mathematics
MAT223H1
Fabian Parsch
MAT223H1 Chapter Notes - Chapter 1.4: H Street
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ApplicationsofLinearSystemsSomeotherphysicalconditionscanbeimposedonthe1TrafcFlowproblemtoreducethesolutionset.OneofthemostdirectapplicationsoflinearsystemsistoForexample,allowsmustbepositive,therefore,studytrafcowswithina...

Mathematics
MAT223H1
Fabian Parsch
ANT100Y1 Chapter Notes - Chapter 1: Semiotic Anthropology, Evolutionary Anthropology, Colin Chapman
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Text Book: Introduction to EVOLUTIONARY ANTHROPOLOGY Author: Shawn M. Lehman Text Book Notes Chapter 1: Introduction to Evolutionary Anthropology Anthropology: is a holistic study of human culture and biology. Com...

Anthropology
ANT100Y1
Max Friesen

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