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Fundamental Rank Theorem
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Classroom Contents
Linear Equations
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- 1 Elementary Matrix
- 2 Unnecessary operation ?
- 3 What is Rank?
- 4 Outer Product
- 5 Fundamental Rank Theorem
- 6 Rank A^T = Rank A
- 7 Product of elementary matrices
- 8 LU factorization
- 9 Inverse of matrix
- 10 Invertible matrix
- 11 Inverse Transformation
- 12 Homogeneous and Particular Solution
- 13 Gaussian Elimination
- 14 Why Gaussian Elimination works
- 15 Row Reduction
- 16 Uniqueness of Reduced Row Echelon Form
- 17 Nul A Col A Rank A
- 18 Basis and dimension
- 19 Existence of Solutions
- 20 Systems and Pivots
- 21 Basis Extension
- 22 Recovering a matrix
