Linear Systems of Equations, Elementary Operations on a Linear System, Gauss Elimination Method, Matrices, Elementary Operations on a Matrix, Multiplication of Matrices, Transpose, Rank, Elementary Matrices, Inverse of a Matrix, LU-Decomposition of a Matrix, Determinants, Properties of Determinant, Cramer’s Rule, Eigenvalues and Eigenvectors, Cayley-Hamilton Theorem and Applications, Linear Combination of Vectors, Subspaces, Linear Independence and Basis, Theorem of Bases, Linear Programming, Geometrical Approach to Linear Programming Problems, The Duality Principle, The Simplex Method with Mixed Constraints, Graphs, Graph Modeling and Applications, Paths, Cycles, and Trees, Subgraphs. Graph Operations, Graph Isomorphism.

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