Notation for row operations (linear algebra)

[edlugie]

I often find that when doing row operations, students will end up doing things like $$R_1+c \cdot R_2 \to R_2$$. This is not really the proper move that's defined in the text. This confusion ends up leading to problems when someone is trying to compute determinants by hand later in the text.

I think that we could learn from computer science here. It's a typical syntax when updating a variable to be its current value with some modification to use the +=, *=, etc syntax. For instance if $$x=5$$ and one takes $x$ += $10$, then now $$x=15$$. In the linear algebra context then, the row operation $$R_1+2R_3 \to R_1$$ could be replaced with $R_1$ += $2R_3$. This is more asymmetric in the role of the two rows, and so I think it would lead to less confusion.