# Determinant - best way of introducing determinants on a linear algebra course

by matqkks
Tags: determinants, linear algebra
 Mentor P: 18,240 Something you absolutely need to do is mention that the determinant is the signed volume of a parallelepiped. That demystifies a lot of properties of the determinants. Also, be sure to mention the history of the determinant: that it was invented to see when systems of equations have a solution and when not. Showing explicitely that the system $$\left\{\begin{array}{ll} ax+by=0\\ cx+dy=0\end{array}\right.$$ has a unique solution if and only if ad-bc=0 is very illuminating. It makes clear why the determinant was invented in the first place: to generalize this to higher dimensions.