Linear Algebra is central to all subjects within mathematics. It is widely used in modelling natural phenomena that are of a linear nature. This course is an introduction to linear algebra and matrix theory. Topics covered include systems of linear equations, determinants and matrix inverses, rank, eigenvalues, and eigenvectors along with their conceptual understanding. Apart from this we will be covering general vector spaces, linear transformations and orthogonality. Some interesting applications will be explored. A unique aspect of this course is the emphasis on the ‘why’ and the ‘how’ of basic notions in linear algebra, such as understanding why the methods we learn work so well or what are the theoretical foundations of abstract notions such as that of a ‘general vector space’. Students will be taught formal proofs of most statements to aid understanding and building of important connections between concepts.