The Solution of Linear Systems AX = B Triangular Systems and Back Substitution Gauss-Jordan Elimination and Pivoting Tri-Diagonal Matrices Inverse Matrix LU Factorization Cholesky, Doolittle and Crout Factorizations Jacobi and Gauss-Seidel Iteration Successive Over Relaxation - SOR Pivoting Methods Iterative Refinement Row Reduced Echelon Form Homogeneous Linear Systems Kirchoff's Law Leontief Model Linear Programming-Simplex Method