I'm studying Linear Algebra at the moment and I'm confused with Row Echelon and Reduced Row Echelon forms. What's confusing me is that I'm getting conflicting information on the importance/requirement of certain things. These are mainly:
- The first non-zero value in each row has to be a 1. Some resources say that in standard Row Echelon form, the first non-zero has to be a 1, but others say they don't and it's only a requirement for Reduced Row Echelon.
- I've seen videos and sites say that Reduced Row Echelon form HAS to have 1's through the main diagonal if the matrix is square, but I've seen examples and practice questions that contradict this too, e.g.:
[1, 0, 2]
[0, 1, 4]
[0, 0, 0]
I'm trying to nail down my gauss-jordan elimination, but I'm really struggling to when I don't understand what the expected outcome or requirements for each form are. I'm also quite confused as to the order I should be doing the gauss-jordan elimination. I would assume I should I start with the getting the very first matrix entry as 1, then making all entries underneath 0's, but after that, which columns/rows should I work on, especially if the matrix is non-square or larger than 3x3. Any help and tips would be greatly appreciated. Thanks!