I'm reading this text and I'm a bit confused about how they determined the determinant of this matrix:
The factoring out of the -7 and the -3 is because of rule 2 in theoreum 3.3 right?
What is the intuition behind these rules? Aren't row operations supposed to keep matrices equal? Aren't matrices that result from the elementary row operations supposed to be equivalent? So why would that change the determinants if you say interchange two rows?