Last class introduced the objects that will motivate our study of linear al- gebra for the rst few classes. Speci cally, we saw de nitions of linear equa- tions, linear systems, and solutions of linear systems. We also saw how to form matrices from linear systems, which are notationally useful when trying to determine solution sets. Eventually we will study matrices for their own sake, but for the time being we will stick with the motivation provided by systems of linear equations. 1 0 0 s1 b1 c1 b2 c2 b3 c3 b4 c4. However, this ideal form results in a system that has a unique solution, and another thing we saw last class was that it is possible for a system to have: 1: a single solution, in nitely many solutions, no solutions. These are the questions we will answer this class (the material for this lecture roughly corresponds to the section rref in the text).