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Investigation of systems of linear equations and matrices. Matrix operations, inverse matrix, partitioned matrices, matrix factorizations. Vector space and subspace of R^n. Null and Column spaces of matrices. Eigenvalues and eigenspaces of matrices. Orthogonal vectors, Least-Squares problems, Diagonaliztion, Quadratic forms, Singular value decompositions. Applications such as Markov chains, computer graphics, electric circuits, and image processing. Mathematics majors should take MTH 310 rather than MTH 301. Students cannot receive credit for both MTH 301 and MTH 310. Prerequisite(s): MTH 218.