MHB Determinants in Introductory Linear Algebra Courses

[matqkks]

How important are determinants in a first course on Linear Algebra.
In some books it is covered very early after an introduction to matrix algebra but in others it is left to the chpater before eigenvalues and eigenvectors. What is the most appropriate place to situate this topic considering students have never covered linear algebra before?

 

[Ackbach]

Determinants can be useful early on in solving systems of equations. However, their real utility is more theoretical, with a nod towards computing eigenvalues. I would definitely say that a first course should cover them. When you cover them, though, is another matter. How many times per week does your class meet? For how many weeks?

If, for example, you are teaching a 4-hour class (meets 4 hours per week), for an entire semester (14 or 15 weeks), and you fail to cover determinants, you should be shot, dead, buried, resurrected, and shot again. On the other hand, if you're doing a class that meets for two hours per week for 5 weeks, perhaps you might focus on other things.