Linear Algebra 2.2 Evaluating Determinants by Row Reduction

My notes are available at asherbroberts.com/ (so you can write along with me).
Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul

[@M3lCHOR]

Amazing videos!!

[@carlzeini9208]

in theorem 2.2.5 example 2, for the 3x3 matrix once you subtract r2 by 4r1 and r3 by 2r1 you still don't get a full row or column of 0s because row 1 is still complete since the x3 values don't cancel each other out so why is the determinant still 0

[@asherroberts]

For that matrix, the second column can be obtained by multiplying the first column by -2.