Other than that ERO's don't change the solution space, you mean?Using the transitive or substitution property to solve a system of equations is on solid ground because those can be taken as postulates. However there is no elimination postulate, is there?
I suppose so. It doesn't seem like a good idea to introduce unnecessarily complicated notation, though.Also if you don't write y=x+4 and y=2x like so but instead as
f(x)=x+4 and g(x)=2x
then if you add and get
and then write it as
then we are implicitly setting f(x)=g(x) right?
The way I do things, is that I write out the matrix each time, and I just have a little note saying something like which means that I take times row one, add it to row two, and store the result in row two.I guess by using the same letter, y, for each line is just a shortcut for not having to explain what is really going on. Prof. Jerison mentions this "sloppiness" in the first lecture of MIT's OCW Calculus.