Transcription of Math 2331 { Linear Algebra
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Math 2331 { Linear Algebra
The Dimension of a Vector SpaceMath 2331 Linear The Dimension of a Vector SpaceJiwen HeDepartment of Mathematics, University of jiwenhe/math2331 Jiwen He, University of HoustonMath 2331, Linear Algebra1 / The Dimension of a Vector SpaceDimension Basis The Dimension of a Vector SpaceThe Dimension of a Vector Space: TheoremsThe Dimension of a Vector Space: DefinitionThe Dimension of a Vector Space: ExampleDimensions of Subspaces ofR3 Dimensions of Subspaces: TheoremThe Basis TheoremDimensions of ColAand NulA: ExamplesJiwen He, University of HoustonMath 2331, Linear Algebra2 / The Dimension of a Vector SpaceDimension Basis TheoremThe Dimension of a Vector Space: TheoremsTheorem (9)If a vector spaceVhas a basis ={b1.}
Jiwen He, University of Houston Math 2331, Linear Algebra 8 / 14. 4.5 The Dimension of a Vector Space DimensionBasis Theorem Dimensions of Subspaces: Theorem Theorem (11) Let H be a subspace of a nite-dimensional vector space V. Any linearly independent set in H can be expanded, if necessary, to a
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