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Lec 1 | MIT 18.06 Linear Algebra, Spring 2005 2. Elimination with Matrices. 3. Multiplication and Inverse Matrices Lec 4 | MIT 18.06 Linear Algebra, Spring 2005 5. Transposes, Permutations, Spaces R^n 6. Column Space and Nullspace 7. Solving Ax = 0: Pivot Variables, Special Solutions 8. Solving Ax = b: Row Reduced Form R 9. Independence, Basis, and Dimension 10. The Four Fundamental Subspaces 11. Matrix Spaces; Rank 1; Small World Graphs 12. Graphs, Networks, Incidence Matrices 13. Quiz 1 Review 14. Orthogonal Vectors and Subspaces 15. Projections onto Subspaces 16. Projection Matrices and Least Squares Lec 17 | MIT 18.06 Linear Algebra, Spring 2005 18. Properties of Determinants 19. Determinant Formulas and Cofactors 20. Cramer's Rule, Inverse Matrix, and Volume Lec 21 | MIT 18.06 Linear Algebra, Spring 2005 22. Diagonalization and Powers of A 23. Differential Equations and exp(At) Lec 24 | MIT 18.06 Linear Algebra, Spring 2005 Lec 24b | MIT 18.06 Linear Algebra, Spring 2005 Lec 25 | MIT 18.06 Linear Algebra, Spring 2005 26. Complex Matrices; Fast Fourier Transform 27. Positive Definite Matrices and Minima Lec 28 | MIT 18.06 Linear Algebra, Spring 2005 Lec 29 | MIT 18.06 Linear Algebra, Spring 2005 30. Linear Transformations and Their Matrices Lec 31 | MIT 18.06 Linear Algebra, Spring 2005 32. Quiz 3 Review 33. Left and Right Inverses; Pseudoinverse 34. Final Course Review

This series of videos covers the fundamentals of linear algebra, including solving systems of linear equations, linear combinations, and multiplying matrices by vectors. It also explains how to draw pictures to represent the algebra and geometry of linear combinations, how to solve three-dimensional linear equations, and how to think of matrix multiplication as a linear combination of the columns of the matrix. Finally, it discusses the concept of nine vectors in nine dimensional space and how it relates to linear algebra.
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