Ax = b and the Four Subspaces (M-I-T)

• An Overview of Key Ideas (M-I-T)
• Elimination with Matrices (M-I-T)
• Multiplication and Inverse Matrices (M-I-T)
• Factorization into A = LU (M-I-T)
• Transposes, Permutations, Vector Spaces (M-I-T)
• Column Space and Nullspace (M-I-T)
• Solving Ax = 0: Pivot Variables, Special Solutions (M-I-T)
• Solving Ax = b: Row Reduced Form R (M-I-T)
• Independence, Basis and Dimension (M-I-T)
• The Four Fundamental Subspaces (M-I-T)
• Matrix Spaces; Rank 1; Small World Graphs (M-I-T)
• Graphs, Networks, Incidence Matrices (M-I-T)