This course covers the fundamentals of linear equations, including elementary matrices, rank, LU factorization, inverse matrices, Gaussian elimination, basis and dimension, and systems of equations. By the end of the course, students will be able to solve linear equations, understand matrix operations, and apply various methods to manipulate matrices effectively. The teaching method includes theoretical explanations, practical examples, and problem-solving exercises. This course is designed for individuals interested in gaining a strong foundation in linear algebra and matrix operations.
Overview
Syllabus
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.
Taught by
Dr Peyam
