Matrices. Elementary Row Operations. Systems of Linear Equations. Gauss-Jordan Elimintaion Method. Square Matrices. Determinants. Invertible Matrices. Vector Spaces. Subspaces. Linear Independence. Basis and Dimension. Linear Transformations. Algebra of Linear Transformations. Isomorphism. Representation of Linear Transformations by Matrices. Linear Functionals. Algebra of Polynomials. Lagrange Interpolation. Prime Factorization of Polynomials.