Course Description
This course introduces the fundamental concepts of linear algebra, emphasizing both theoretical foundations and practical applications. Topics include systems of linear equations, matrix algebra, vector spaces, linear transformations, determinants, eigenvalues, eigenvectors, inner products, orthogonality, and least squares solutions. Applications in data science, engineering, and modeling (e.g., Markov chains, data fitting) are integrated to connect theory to real-world problems. The course is designed for students in mathematics, engineering, computer science, and related fields.

Learning Objectives
By the end of this course, students will be able to:

• Solve systems of linear equations using Gaussian elimination and matrix methods (Quizzes, Problem Sets, Midterm, Final)
• Perform matrix operations and compute determinants and inverses (Quizzes, Problem Sets, Midterm, Final)
• Understand and apply concepts of vector spaces, linear transformations, and bases (Problem Sets, Midterm, Final)
• Compute eigenvalues and eigenvectors and apply them to problems like diagonalization (Problem Sets, Midterm, Final)
• Use inner products, orthogonality, and least squares to solve applied problems (Computational Labs, Final)
• Connect linear algebra concepts to applications in data science and engineering (Computational Labs, Problem Sets)