MA 26500
Linear Algebra
Summer 2018
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Lesson 1 1.1 Systems of Linear Equations
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Lesson 2 1.2 Row Reduction and Echelon Forms
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Lesson 3 1.3 Vector Equations
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Lesson 4 1.4 & 1.5 The Matrix Equation \(Ax = b\) & Solution Sets of Linear Systems
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Lesson 5 1.7 & 1.8 Linear Independence & Introduction to Linear Transformations
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Lesson 6 1.9 The Matrix of Linear Transformation
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Lesson 7 2.1 Matrix Operations
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Lesson 8 2.2 & 2.3 The Inverse of a Matrix
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Lesson 9 2.8 Subspaces of \(\mathbb{R}^n\)
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Lesson 10 2.9 Dimension and Rank
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Lesson 11 3.1 & 3.2 Determinants
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Lesson 12 3.3 Cramer's Rule, Volume, and Linear Transformations
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Lesson 13 4.1 Vector Spaces and Subspaces
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Lesson 14 4.2 Null Space, Column Space, and Linear Transformations
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Lesson 15 4.3 Linear Independence Sets and Bases
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Lesson 16 4.5 The Dimension of a Vector Space
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Lesson 17 4.6 Rank
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Lesson 18 5.1 & 5.2 Eigenvectors, Eigenvalues, and Characteristic Equations
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Lesson 19 5.3 Diagonalization (Part 1)
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Lesson 20 5.3 Diagonalization (Part 2)
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Lesson 21 5.4 Eigenvectors and Linear Transformations
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Lesson 22 Appendix and 5.5 Complex Eigenvalues
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Lesson 23 5.7 Applications to Differential Equations
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Lesson 24 6.1 Inner Product, Length, and Orthogonality
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Lesson 25 6.2 Orthogonal Sets
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Lesson 26 6.3 Orthogonal Projections
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Lesson 27 6.4 The Gram-Schmidt Process
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Lesson 28 6.5 Least-Squares Problems
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Lesson 29 6.7 Inner Product Spaces
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Lesson 30 7.1 Diagonalization of Symmetric Matrices (part 1)
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Lesson 31 7.1 Diagonalization of Symmetric Matrices (part 2)