In some literature on linear algebra determinants play a critical role and are emphasized in the earlier chapters. (See books by Anton & Rorres, and Lay). However in other literature it is totally ignored until the latter chapters. (See Gilbert Strang).

How much importance should we give the topic of determinants . I tend to use it to find linear independence of vectors and might extend this to finding the inverse but I think Gauss Jordan and LU might be easier for inverse. Does it have any other uses in Linear Algebra.

Are there areas where determinants are used and have a real impact? Are there any real life applications of determinants?

Is there a really good motivating example or explanation which will hook students into this topic?