In most of the LA courses determinants just... feel almost completely unmotivated, their definition just "comes down from the heavens in all its mysterious glor

In most of the LA courses determinants just... feel almost completely unmotivated, their definition just "comes down from the heavens in all its mysterious glory", and wow, how convenient that those things have all those nice properties!.. although they don't seem to actually be used for much unless your LA course actually contains elements of elimination theory which most of them don't, for some reason (even though it would seem to be quite a useful part of mathematical knowledge but apparently not).