I don't know if this is just me or a few other students as well, but I'm having difficulty putting a given matrix in RREF/REF. In my classes or review sessions, the professor easily does all the Gaussian eliminations to get a RREF/REF---and only then it makes sense to me. But for a few problems, if I were to do it on my own, I sometimes don't see how one can easily find the forms.
Is there a simple trick, or a 'simple' trick with multiple steps? Anything I should ALWAYS start out with? Etc. Examples would be great!
Cheers.
My best simple trick is to try to start with a matrix that has the leftmost non-zero entry at the top of the matrix, then trying to remove all entries in the leftmost nonzero entry's column in the rows beneath it with linear combinations of that row and the rows beneath it. Continue to do this until there is only one non-zero leading entry in that column, then continue doing the same for all columns to the right of it that have a leading column. Don't get too worried if the matrix isn't upper triangular as you work, as you can always swap rows! Cheers!