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First published on Thursday, Aug 27, 2026 and last modified on Tuesday, Sep 1, 2026
Lecture 1 - Introduction to Linear Algebra I
Welcome to our first course of Linear Algebra, with a focus on linear systems and matrices.
Upon completion of this course, you will gain a comprehensive understanding of Gaussian Pivot, its Gauss Jordan variant, and their applications to all types of systems of linear equations, regardless of their number of solutions.
You will also develop the skills to work with matrices and both line and column vectors, performing algebraic operations, inverting matrices and calculating determinants.
Additionally, you will learn to decompose an invertible square matrix into the product of a lower triangular matrix and an upper triangular matrix, known as LU factorization, bridging the concepts of Gaussian elimination and matrix operations.
All techniques for solving linear systems and manipulating matrices and vectors are designed for dimensions beyond three or four, primarily in the context of computer implementation.
To facilitate this, we provide numerous Python scripts that are thoroughly explained in the accompanying videos.
We highly recommend that you complete the free MathEdu course 'Scientific Computing with Python: The Basics' prior to starting this linear algebra course.
This small investment of time will yield significant benefits in your learning journey.
Scientific Computing with Python: The Basics
So are you ready to explore the course? 'Linear Algebra I: Linear Systems and Matrices'.
Linear Algebra I: Linear Systems and Matrices