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Rank Theorem (Part 2)
by Carol Braun
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Rank Theorem (Part 1)
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Overview Of Lesson In On Rank
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Dimension Of Null Space And Column Space
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Isomorphism And Coordinate Systems In Other Vector Spaces
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Using Bases To Define Coordinate Systems
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Finding A Basis For A Column Space
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Formal Definition Of A Basis
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What Is A Basis?
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Linear Independence And Dependence In Any Vector Space
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Range And Column Space
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Null Space (Kernel) Of A Linear Transformation
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Null Spaces
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Subspaces
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Example Of A Vector Space: Real-Valued Functions On The Set Of Reals
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Axiomatic Definition Of A Vector Space
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Determinant As Scaling Factor ("Size" Of Image)
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Determinant As Area Of Parallelogram
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Example Using Inverse Formula
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Formula For Inverse Based On Cramer's Rule
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Introduction To Cramer's Rule
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Examples With Partitioned Matrices
Intro To Partitioned Matrices
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Video Lecture #1: The Invertible Matrix Theorem
