This course introduces the fundamental concepts of Linear Algebra. Key topics include Vector Spaces and subspaces, linear combinations, and solving systems of linear equations. Students will explore Linear Dependence and Independence, defining Bases and Dimension, and working with Maximal Linearly Independent Subsets. The course thoroughly covers Linear Transformations, their Null Spaces and Ranges, and Matrix Representation. A significant portion is dedicated to Matrix Rank, Elementary Transformations, Normal Form, and different types of Systems of Linear Equations (homogeneous and non-homogeneous). Finally, students will learn about Eigen values, Eigen vectors, their properties, and the Cayley-Hamilton Theorem. This subject provides essential mathematical tools used across various scientific and engineering disciplines.
- Teacher: Mr ALBIN MATHEW