About this course

This introductory course provided by UPValencia X dives into the fundamentals of algebra and matrix theory, focusing on systems of linear equations, matrix operations, and their applications. Starting with a revision of single-variable equations, the course progressively covers advanced topics including matrix inverses and determinants, equipping students with the mathematical tools needed in further scientific and engineering contexts.

Course Features

• Institution: UPValenciaX
• Subject: Math
• Level: Introductory
• Prerequisites: Basic understanding of real number operations, equations, unknowns, and solutions.
• Language: English
• Video Transcript: English

What you'll learn

• Fundamentals and classifications of systems of linear equations.
• Introduction to matrices and matrix operations.
• Techniques for calculating inverse matrices and determinants.
• Understanding the relationship between matrix operations and solutions to linear equations.

Course Coverage

• Introduction to equations with a single unknown and methods for solving them.
• Detailed exploration of systems of linear equations, including Gauss' method.
• Introduction and application of matrix concepts and operations.
• Methods for calculating inverse matrices using Gaussian and adjoint methods.
• Detailed understanding of matrix equations and their implications.
• Learning to calculate the determinant of a square matrix.
• Studying the rank of a matrix.
• Utilizing Cramer's rule in the matrix expression of systems of linear equations.

Who this course is for

Students, early career engineers, and professionals in related scientific fields looking to enhance their understanding of linear algebra and matrix operations, as well as anyone interested in learning the mathematical foundations necessary for advanced studies in engineering, physics, or computer science.

Real-World Application

Knowledge gained in this course can be applied in various real-world contexts such as developing algorithms for software applications, solving engineering problems, performing economic modeling, and conducting scientific research where linear equations and matrix manipulations are fundamental.