Linear Equations

Learn the fundamentals of linear equations in this comprehensive 4.5-hour course. Explore key concepts such as elementary matrices, rank, outer product, and the Fundamental Rank Theorem. Dive into matrix operations, including LU factorization and matrix inversion. Understand homogeneous and particular solutions, Gaussian elimination, and row reduction techniques. Examine the relationship between null space, column space, and rank. Investigate basis and dimension, solution existence, and the importance of pivots in linear systems. Master the process of basis extension and matrix recovery, gaining a solid foundation in linear algebra principles.

Elementary Matrix.
Unnecessary operation ?.
What is Rank?.
Outer Product.
Fundamental Rank Theorem.
Rank A^T = Rank A.
Product of elementary matrices.
LU factorization.
Inverse of matrix.
Invertible matrix.
Inverse Transformation.
Homogeneous and Particular Solution.
Gaussian Elimination.
Why Gaussian Elimination works.
Row Reduction.
Uniqueness of Reduced Row Echelon Form.
Nul A Col A Rank A.
Basis and dimension.
Existence of Solutions.
Systems and Pivots.
Basis Extension.
Recovering a matrix.