جبر خطي - LINEAR ALGEBRA

linear systems of equations (homogenous and non-homogenous) with full details (matrix equation, determinants, properties of determinants, Cramer’s rule, matrix inverse, solution of linear systems using inverse matrix, properties of matrices, Gauss elimination method, augmented matrix, Gauss Jordan method, Echelon form, rank of the matrix of coefficients and the nature of solutions. Vector spaces, linear combinations linear dependent and independent vectors, subspaces, bases, dimensions, linear transformations, the four fundamental subspaces. The eigenvalues, eigenvectors, Eigen space, Cayley Hamilton theorem.