Determinants were defined when mathematicians were looking for formulae to solve Systems of Linear Equations during the early 19th century. As we shall see, the notation and properties of determinants follow directly from solving systems of equations. The 19th century was a time in mathematical history where new notations were being created at a rapid pace. The determinant notation was used to describe a sequence of computation, and thereby make solving systems more efficient. Once the concept and notation for the determinant were accepted, many other uses for determinants were discovered. The second abstraction is to view the determinant as a function from the set of nxn matrices into the real numbers. The determinant function generates a useful partition of the set of nxn matrices.