MX4 column ops and right-multiplication?

[StevenClontz]

Continuing discussion from #325

Me:

I'm also somewhat interested in mixing in column operations and right-mulitiplication as well.

@siwelwerd

As far as column operations/right multiplication, I'm more hesitant because they aren't really well motivated at this point. I guess they could be motivated in EV6 via activities as ways to simplify the collection of vectors in a spanning set, eventually to produce a basis? That seems like a bigger change worthy of a separate isssue.

I find the column thing comes up organically: we actually don't motivate why you need to left-multiply by the elementary matrix to get row operations, so it's natural to see what happens when you do it on the right. So while students know there's a reason to do row operations, they can easily discover that column operations are done with right-multiplication, and I think it's okay to defer that application to the next learning outcome while still having them practice using matrices to model the operations.