Update 2024-07-27-rref.md

_posts/2024-07-27-rref.md

@@ -38,8 +38,6 @@ toc:
   - name: Kernel determines RREF
 ---
 
-(This is a first draft, subject to change.)
-
 I've stood by and let this go on for too long. As someone who has been tutoring/teaching linear algebra for five years now, I've looked at the subject as a whole through multiple different perspectives. We have this abstract difficult subject with a million terms and concepts (many terms actually being the SAME concept under a different name), problems that can look entirely different but end up asking the exact same question, AND most students have to figure it out while they are learning how to properly do a mathematical proof for the first time (which is NOT an easy skill to learn). No wonder people struggle with it! And, so, I can understand why many professors choose to offload the concepts and underlying "algebra" until later in the course, and start off with "Here's a system of equations, row reduce it!" for three weeks. And though tedious, and generally unmotivated, it's certainly... easy?
 
 The problem is that with so much to cover, my experience with most students is that the key concepts that tie EVERYTHING together are not being emphasized. So when the more important topics like basis, linear independence, span, coordinate vectors, kernel, image, etc. are introduced, the pathways between the new topic and what the student has already learned aren't being drawn, and it all seems so disconnected. More like you're learning something completely different solved with a similar method, rather than learning an extension of a previous concept.