Difference between REF/RREF (Gauss vs Gauss-Jordan)?

[leo255]

Hi all,

Just started my Linear Algebra class like a month ago. I have been going through my book, as well as other resources, but I am still confused by this. I have a decent grasp of how to row reduce, and, in general, know that I need to get the 1's in a diagonal line, with 0's everywhere else.

Also, when you row reduce, should you go through the same algorithm/procedure every time? In other words, should you try to get the first "1," and then move to the second and third row's, to try to get "0"s in the first spot (instead of working on a "0" in a different spot?

I'm really new to this subject, so I apologize for the noob question. Thanks!

 

[Mark44]

Hi all,

Just started my Linear Algebra class like a month ago. I have been going through my book, as well as other resources, but I am still confused by this. I have a decent grasp of how to row reduce, and, in general, know that I need to get the 1's in a diagonal line, with 0's everywhere else.

It helps to understand what the acronyms mean -- otherwise they're just bunches of meaningless letters.
REF - row echelon form. The leading nonzero entry in any row is 1, and there are only 0's below that leading entry.
RREF - reduced row echelon form. Same as REF plus there are only 0's above any leading entry.

Also, when you row reduce, should you go through the same algorithm/procedure every time?

Pretty much, although it's sometimes helpful to switch one or more pairs of rows. Otherwise, you start at the leftmost column, eliminate the entries above and below it and continue in that fashion.

In other words, should you try to get the first "1," and then move to the second and third row's, to try to get "0"s in the first spot (instead of working on a "0" in a different spot?

I'm really new to this subject, so I apologize for the noob question. Thanks!