This course is a study of the theory of matrices and applications of systems of linear equations. Topics include systems of linear equations, matrices and matrix algebra, vectors and vector spaces, linear independence, span of a set of vectors, basis and dimension of a vector space, linear transformations of vector spaces, rank of a matrix and the Rank Theorem, determinants and their properties, eigenvalues and eigenvectors, diagonalization of matrices, inner products, orthogonal basis, Gram-Schmidt Orthogonalization, and orthogonal projection of a vector onto a subspace. Prerequisite: Successful completion of MTH 222 Calculus 2 or higher. 3 cr. 3 Lec.