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Welcome to Linear Algebra
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Linear Algebra - Foundational Concepts and Transformations
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- 1 Welcome to Linear Algebra
- 2 Systems of Linear Equations
- 3 Geometric meaning of solutions to a linear equation in 2D
- 4 Geometric meaning of a linear system in 2D
- 5 Vectors, both Algebraically and Geometrically
- 6 Linear Combinations and Span -- Part I
- 7 Linear Combinations and Span -- Part II
- 8 How does 1:1 and onto relate to invertibility?
- 9 Invertible Transformations
- 10 Subspaces of R^n
- 11 Null Space and Column Space of a Matrix
- 12 Gridlines in nonstandard coordinate systems.
- 13 Writing Vectors in Different Coordinate Systems
- 14 Finding the Dimension of a Subspace
- 15 Rank, and the Relationship between Col(A) and Null(A)
- 16 Visualizing a vector in multiple coordinate systems
- 17 Deriving the Change-of-Basis formula
