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Watch the 1st video of the course

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Lecture 1: The Geometry of Linear Equations.

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Lecture 2: Elimination with Matrices.

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Lecture 3: Multiplication and Inverse Matrices.

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Lecture 4: Factorization into A = LU

There is finally a better version of this lecture! https://www.youtube.com/watch?v=MsIvs_6vC38&index=4&list=PLE7DDD91010BC51F8

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Lecture 5: Transposes, Permutations, Spaces R^n.

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Lecture 6: Column Space and Nullspace.

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Lecture 7: Solving Ax = 0: Pivot Variables, Special Solutions.

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Lecture 8: Solving Ax = b: Row Reduced Form R.

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Lecture 9: Independence, Basis, and Dimension.

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Lecture 10: The Four Fundamental Subspaces.

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Lecture 11: Matrix Spaces; Rank 1; Small World Graphs.

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Lecture 12: Graphs, Networks, Incidence Matrices.

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Lecture 13: Quiz 1 Review.

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Lecture 14: Orthogonal Vectors and Subspaces.

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Lecture 15: Projections onto Subspaces.

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Lecture 16: Projection Matrices and Least Squares.

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Lecture 17: Orthogonal Matrices and Gram-Schmidt.

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Lecture 18: Properties of Determinants.

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Lecture 19: Determinant Formulas and Cofactors.

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Lecture 20: Cramer's Rule, Inverse Matrix, and Volume.

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