Right at the end of last class we learned hwo to write the solution sets of linear systems in vector parametric form, and i mentioned some terminology related to parts of the vector parametric form. Recall that we solved the linear system (here written in the form of a. 2 matrix equation) (cid:20)6 whose solution set is . The part of the vector parametric solution involving parameters is called the homogeneous solution and the vector that isn"t multiplied by any parameters is called the particular solution. A homogeneous linear system is one of the form. 1 where a in m n and (cid:126)0 = So basically, homogeneous systems are just that subclass of linear sys- tems consisting of equations whose constant terms are all equal to 0. These systems are singled out for special attention because unlike general linear sys- tems, which can consistent or inconsistent, homogeneous systems are never inconsistent they always have at least one solution.