Okay so I'm a first year engineering student and I'm taking linear algebra. I understand how to take determinants of nxn matrices, and I know how to do co-factor expansion. But I still don't understand what a determinant is. I don't like learning algorithms on how to do certain things in math without knowing why it works. I hope someone can answer the "Why?" question for me. To keep is simple as possible: What the hell is a determinant?