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This article explains the fundamental theorems on matrix rank, distinguishes homogeneous and non‑homogeneous linear systems, introduces augmented matrices, and outlines a step‑by‑step Gaussian elimination method to find solutions of linear equations.
This article explains elementary row and column transformations, matrix equivalence properties, row‑reduced forms, equivalence classes, minors, rank definition and its properties, and distinguishes homogeneous from non‑homogeneous linear systems, providing a comprehensive overview of fundamental linear algebra concepts.
This article explains the stability criteria for first‑order and second‑order linear difference equations with constant coefficients, shows how to compute equilibrium points, and extends the analysis to higher‑order systems and nonlinear cases by linearization, providing clear conditions based on characteristic roots.