A unified linear algebraic approach to adaptive signal processing (ASP) is presented. Starting from just Ax=b, key ASP algorithms will be derived in a simple, systematic, and integrated manner without requiring any background knowledge to the field. Algorithms covered will be steepest descent, LMS, Normalized LMS, Kaczmarz, Affine Projection, RLS, Kalman filter, and MMSE/Least Square Wiener filters. By following this approach, readers will discover a synthesis; that one and only one equation is involved in all these algorithms. By mastering this one equation, they will be able to master the fundamental algorithms of ASP in minimum amount of time with a minimum effort. They will also learn the connection of this equation to more advanced algorithms like reduced rank adaptive filters, extended Kalman filter, particle filters, multigrid methods, preconditioning methods, Krylov subspace methods and conjugate gradients. This will enable them to enter many sophisticated realms of modern research and development. Eventually, this one equation will not only become their passport to ASP but also to many highly specialized areas of computational science and engineering.