Techniques of Linear Algebra

Linear Algebra Course-Master the Fundamentals and BeyondThis comprehensive linear algebra course is designed to provide a solid foundation in one of the most essential branches of mathematics, with a strong focus on both theory and practical problem-solving skills. Whether you're a university student in engineering, computer science, or mathematics-or even a high school student preparing for advanced studies-this course will guide you through the key concepts and techniques of linear algebra in a clear and structured way. You will start by exploring the fundamental building blocks such as determinants and matrices and learn how to apply them in solving linear and non-linear systems of equations.

We will also cover important algebraic tools like partial fractions and the binomial theorem, which frequently appear in engineering and applied mathematics problems. As you progress, you'll dive into more advanced topics such as eigenvalues and eigenvectors, LU factorization, and linear combinations, all of which are crucial in fields like machine learning, structural analysis, and control systems. We'll also discuss mathematical induction, a powerful method of proof, and the theory of equations, giving you a broader mathematical perspective.

Each topic is taught with step-by-step explanations, practical examples, and guided problem-solving strategies to help you build confidence and mastery. By the end of the course, you'll have the tools and mindset needed to tackle complex problems with ease.