I'm asking this as a general question. Usually when I'm asked to find rank I am totally confused as to how to proceed at all. None of the transformations behind don't make sense to me.
Is there a standard like, procedure, that you can always use to get to the result if you have absolutely no smart ideas whatsoever as to which elemental transformations to use? What is the purpose of a rank (e.g. in solving systems of equations by Kronecker-Capelli)? What are we trying to obtain?
I am mainly given those with parameters (up to three) and that gets even more confusing.
Thanks for answers.
PS I'd be satisfied with some links being provided addressing the matter (techniques and such)
By elementary row operations reduce as many rows as you possibly can, count the number of non-zero rows.
If you are not sure if you have reduced as far as possible, put the matrix into "row echelon" form.