Linear Algebra: Matrix Algebra, Determinants, & Eigenvectors

The Matrix Algebra module provides an in-depth exploration of matrix operations, inverse matrices, and the characterization of invertible matrices. Learners will engage in practical exercises to reinforce their understanding, preparing them for advanced applications of matrix algebra.

The Subspaces module delves into the properties of subspaces of R^n, introducing learners to the concept of dimension and rank. Through practical exercises, learners will gain a comprehensive understanding of subspaces and their relevance in linear algebra.

The Determinants module offers insights into the fundamental properties of determinants, including Cramer's Rule, volume, and their applications in linear transformations. Practical exercises will reinforce learners' understanding of determinants and their practical significance.

The Eigenvectors and Eigenvalues module explores the essential concepts of eigenvalues and eigenvectors, delving into the characteristic equation and their practical applications. Learners will engage in exercises to solidify their understanding of these crucial concepts.

The Diagonalization and Linear Transformations module provides in-depth knowledge of diagonalization, eigenvectors, and linear transformations. Practical exercises will enable learners to apply these concepts effectively, preparing them for real-world applications.

The Final Assessment module serves as a comprehensive evaluation of the knowledge and skills acquired throughout the course, ensuring learners have mastered the advanced concepts of matrix algebra, determinants, and eigenvectors.