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Linear Equations

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Overview

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This course develops foundational linear algebra through matrices, rank, inverses, LU factorization, Gaussian elimination, systems of equations, and vector spaces. It also explains bases, dimensions, pivots, and conditions for the existence and uniqueness of solutions.

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

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