Course Contents

Definition of matrix. various types of matrices, Algebra of matrices, Determinant of square matrix, cofactors and minors, Laplace expansion of determinants, Elementary matrices, adjoint and inverses of matrices, Rank of a matrix, Introduction to systems of linear equations, Cramer’s rule, Guassian elimination and Gauss Jordan method, solution of homogeneous and non-homogeneous linear system of equations, Vector spaces, Subspaces, Linear combination and spanning set, Linear independence and linear dependence, basis and dimension, Row space, Colum space and Null space, Linear transformation, Matrices of linear transformations, Rank and nullity, Eigen values and Eigen vectors, Diagonalization, Orthogonal matrices, Similar matrices.

Course Learning Outcomes

This course will be proved helpful in having a solid understanding of the essential ideas of different disciplines in mathematics and will prepare the students adequately for encountering a basic course in group theory, rings and modules.