Fair, but I'm still not aware of any practical applications for "systems of equations" like the person I responded to mentioned. If you know any please share.

Fair, but I'm still not aware of any practical applications for "systems of equations" like the person I responded to mentioned. If you know any please share. The determinant intuition for me is the signed volume factor for a change of basis. I've seen the combinatorial lattice path application and I'm sure there are more in other fields. But not much reason I can see to have them feature so prominently in an intro linear algebra class. Better to spend more time with SVD for instance, which wasn't even covered in the first linear algebra class I took.