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Linear Algebra 4.1.1 Vector Spaces
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Linear Algebra
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- 1 Linear Algebra 1.1.1 Systems of Linear Equations
- 2 Linear Algebra 1.1.2 Solve Systems of Linear Equations in Augmented Matrices Using Row Operations
- 3 Linear Algebra 1.2.1 Row Reduction and Echelon Forms
- 4 Linear Algebra 1.2.2 Solution Sets and Free Variables
- 5 Linear Algebra 1.3.1 Vector Equations
- 6 Linear Algebra 1.3.2 Linear Combinations
- 7 Linear Algebra 1.4.1 The Matrix Equation Ax=b
- 8 Linear Algebra 1.4.2 Computation of Ax
- 9 Linear Algebra 1.5.1 Homogeneous System Solutions
- 10 Linear Algebra 1.5.2 Non-Homogeneous System Solutions
- 11 Linear Algebra 1.6.1 Applications of Linear Systems - Economic Sectors
- 12 Linear Algebra 1.6.2 Applications of Linear Systems - Network Flow
- 13 Linear Algebra 1.7.1 Linear Independence
- 14 Linear Algebra 1.7.2 Special Ways to Determine Linear Independence
- 15 Linear Algebra 1.8.1 Matrix Transformations
- 16 Linear Algebra 1.8.2 Introduction to Linear Transformations
- 17 Linear Algebra 2.1.1 Matrix Operations - Sums and Scalar Multiples
- 18 Linear Algebra 2.1.2 Matrix Operations - Multiplication and Transpose
- 19 Linear Algebra 2.2.1 The Inverse of a Matrix
- 20 Linear Algebra 2.2.2 Solving 2x2 Systems with the Inverse and Inverse Properties
- 21 Linear Algebra 2.2.3 Elementary Matrices And An Algorithm for Finding A Inverse
- 22 Linear Algebra 2.3.1 Characterizations of Invertible Matrices
- 23 Linear Algebra 3.1.1 Introduction to Determinants
- 24 Linear Algebra 3.1.2 Co-factor Expansion
- 25 Linear Algebra 3.2.1 Properties of Determinants
- 26 Linear Algebra 4.1.1 Vector Spaces
- 27 Linear Algebra 4.1.2 Subspace of a Vector Space
- 28 Linear Algebra 4.2.1 Null Spaces
- 29 Linear Algebra 4.2.2 Column Spaces
- 30 Linear Algebra 4.3.1 Linearly Independent Sets and Bases
- 31 Linear Algebra 4.3.2 The Spanning Set Theorem
- 32 Linear Algebra 4.5.1 The Dimension of a Vector Space
- 33 Linear Algebra 4.5.2 Subspaces of a Finite Dimensional Space
- 34 Linear Algebra 4.6.1 The Row Space
- 35 Linear Algebra 4.6.2 Rank
- 36 Linear Algebra 5.1.1 Eigenvectors and Eigenvalues
- 37 Linear Algebra 5.1.2 More About Eigenvectors and Eigenvalues
- 38 Linear Algebra 5.2.1 Determinants and the IMT
- 39 Linear Algebra 5.2.2 The Characteristic Equation
- 40 Linear Algebra 6.1.1 Inner Product, Vector Length and Distance
- 41 Linear Algebra 6.1.2 Orthogonal Vectors
- 42 Linear Algebra 6.2.1 Orthogonal Sets
- 43 Linear Algebra 6.2.2 Orthogonal Projections
- 44 Linear Algebra 6.3.1 Orthogonal Decomposition Theorem
- 45 Linear Algebra 6.3.2 The Best Approximation Theorem
- 46 Linear Algebra 6.5.1 Least Squares Problems
