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Introduction to Matrices Introduction and Basic Operations Matrix Multiplication Algebraic Properties of Matrix Operations Invertible Matrices Special Matrices: Triangular, Symmetric, Diagonal Elementary Operations for Matrices Matrix Exponential Applications: Application of Invertible Matrices: Coding Complex numbers as Matrices Markov Chains Systems of Linear Equations System of Equations: An Introduction Systems of Linear Equations: Gaussian Elimination Systems of linear equations in Two variables. Systems of linear equations in Three variables. Application of Determinant to Systems: Cramer's Rule More Problems on Linear Systems and Matrices Determinants Introduction to Determinants Determinants of Matrices of Higher Order Determinant and Inverse of Matrices Application of Determinant to Systems: Cramer's Rule Eigenvalues and Eigenvectors Eigenvalues and Eigenvectors: An Introduction Computation of Eigenvalues Computation of Eigenvectors The Case of Complex Eigenvalues Diagonalization APPENDIX Tables