This year-long course covers various topics in linear algebra including matrix theory, systems of linear equations, row operations, Gaussian elimination, matrix algebra, matrix inverses, determinants, factorization, vector spaces, dependence and independence, linear transformations, eigenvalues, eigenvectors, inner products, orthogonality and least squares, symmetric matrices, and finite-state Markov chains.  Selected applications of linear algebra are included.  The course requires students to be familiar with mathematical proof writing.  This course is a second-year university level course and is offered to students who completed multivariable calculus.