Ah, I left out a lot! But I included enough that you could extend to some relatively deep parts! But among what I omitted was determinants. So, I couldn't me

Ah, I left out a lot! But I included enough that you could extend to some relatively deep parts! But among what I omitted was determinants. So, I couldn't mention your points! To me the one easy approach to determinants is to say that they give a volume, and the volume is zero if and only if there is linear dependence.