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Outline of sections in Linear Algebra, Spring 1999

- Day 1: Systems of linear equations, Row operations
- Day 2: Echelon Form, Pivot and Free variables
- Day 3: Vector equations, Span
- Day 4: Matrix equation, TFAE
- Day 5: Solution sets for systems, homogeneous and nonhomogeneous
- Day 6: Linear Independence, more variables than equations implies
nontrivial solutions to homogeneous system
- Day 7: Linear Transformations
- Day 8: House example, matrix of a linear transformation
- Day 9: 1-1, onto, matrix operations
- Day 10: Inverse
- Day 11: TFAE for invertible matrices
- Day 12: Review for Test 1
- Day 13: Applications to computer graphics
- Day 14: Subspaces (VERY IMPORTANT!! Column space, Null Space); Basis, Coordinate Vector, Rank Theorem
- Day 15: Determinants, Cofactor expansion, Triangular matrix theorem
- Day 16: Properties of Determinants, row operations and determinants, multiplicative property
- Day 17: Cramer's rule, connection to volumes of linear transformations
- Day 18: Abstract definition of Vector space, new example of polynomials
- Day 19: Null Space, Column Space, Kernel, and Range
- Day 20: More on Bases, Spanning set theorem!!
- Day 21: Unique representation theorem, coordinate mapping
- Day 22: Dimension is independent of basis chosen
- Day 23: Rank theorem revisited
- Day 24: Change of basis matrices (very difficult!)
- Day 25: Introduction of Eigenvectors, Eigenvalues (NOT on test)
- Day 26: Review for Test 2