About This Course

Explore the core elements of linear algebra in this intermediate-level course, focusing on systems of linear equations, their solutions, and application strategies. Beginning with the introduction of systems of linear equations, the course advances through methods and algorithms for solving them, building up to the exploration of linear independence and transformations, crucial for applications in various industries.

What Students Will Learn

• Methods to evaluate mathematical expressions involving linear systems.
• Characterization of linear systems by their solution sets and consistency.
• Application of elementary row operations for solving linear system equations.
• Understanding of vector relations through linear combinations and geometric interpretations.
• Insights into linear independence and its implications on linear systems.
• Skills to construct and analyze linear transformations in matrices.
• Ability to determine properties of linear transformations such as injectivity and surjectivity.

Course Prerequisites

Students are expected to have foundational knowledge in algebra, specifically in solving linear equations, understanding the domain and range of functions, basic graphing, and trigonometry. These prerequisites are typically covered in pre-calculus courses.

Course Content

• Introduction to Systems of Linear Equations
• Algorithms for Solving Linear Equations
• Applications of Linear Algebra
• Concepts of Vector Spaces and Span
• Linear Independence and Transformations

Who This Course Is For

This course is designed for individuals interested in gaining a comprehensive understanding of linear algebra, applied mathematicians, engineers, economists, and anyone in the fields of science and technology who deals with mathematical modeling and data analysis.

Real-World Applications

Skills acquired from this course can be applied in various real-world contexts, such as solving complex data problems, enhancing machine learning models, optimizing engineering processes, and conducting economic forecasts and scientific research which require meticulous data interpretations.