We are asked to find the Row-Reduced Echelon Form (RREF) of some augmented coefficient matrices for systems of linear equations. I know how to apply the elementary row operations but what I don't know is that given a question, how you should approach it and what are the correct row operations to perform. Is there a strategy to approach with or is it just trial and error?
Here is the matrix:
Apologies for the augmented section, I couldn't find the right tex for it. Hope it's clear. Anyway I began to approach it by interchanging rows 3 and 1 to get the leading 1 in the top left, then subtracting multiples of the new row 1 to get zeros below, but it got to a point where there wasn't a clear next step. As I understand the RREF is unique, correct? So I don't think I'll neccessarily be able to find it by trial and error?
Also, given the RREF - I am asked to find the vector-parametric solution but again this is not in my notes, nor can I find it online.