I’m happy to say I had another productive week on KA! Having two productive weeks in a row feels pretty good and I’m hopeful I’ll be able to keep this momentum, going forward. I made it through seven videos on KA, but I also watched nine videos from the Essence of Linear Algebra playlist by 3Blue1Brown on YouTube. I made a bit more sense of the videos from 3B1B this week than I did a fews months ago (or maybe a year? 🤔) when I watched them last time, but I can tell I still have a long ways to go before I fully wrap my head around everything that’s covered in those vids. On KA I made it through two sections – they only had five videos between the two of them 🤷🏻‍♂️– and finished the week starting a third. I think I got a decent grasp on what the videos were talking about and how to do the math shown in them, but I don’t understand why the math works from most of those videos. Nonetheless, I feel like I made some solid progress this week understanding linear algebra which I’m pumped about! Fingers crossed I can keep it going next week. 🤞🏼

The first section I worked through this week, titled Linear Dependence and Independence, had three videos in it. In all of the videos, Sal showed the proof behind how to determine if two or more vectors are linearly dependent (LD) or if they’re linearly independent (LI). Here are my notes first explaining what it means for vectors to be LD or LI and then two example questions from the second video:

Question 1

Question 2

The next section I worked through was titled Subspaces and the Basis for a Subspace. The math in these videos was a bit hard to follow along with, but understanding the gist of what a subspace is was super easy to understand. A subspace is simply a subset of a dimension that 1) includes the 0 vector, 2) allows two vectors in that dimension to be added together and stay within that subspace, and 3) allows for any vector in that dimension to be scaled and still fall within that dimension. (FYI the way I phrased that may not be 100% precisely accurate. I’m not sure if dimension and subspace can be used interchangeably here. Probably not.) I understood what the videos were talking about but asked CGPT to sum it up for me and this is what it said:

The last section I started this week (which, by the way, has 13 videos in it 😳) is titled Vector Dot and Cross Products. I only made it through two videos from this section which were both pretty straightforward and essentially review. The main concepts I learned/reviewed were how to add and scale, and multiply them using the dot product. I’m embarrassed to say that by the time I got to the end of Multivariable Calculus I still didn’t really understand how or when to use dot product vs how or when to use the cross product, or even what the difference between the two operations was. (And to be fair, I still don’t really understand… 😒) So even though the two videos I watched from this section seemed like review and were pretty easy to follow along with, it was definitely helpful to watch them, and I’m hopeful that this section will help me FINALLY wrap my head around these types of vector operations. Here are two screen shots from those videos and some notes I took:

Finally, just to fill out this post a bit more, here are the nine videos I watched from the 3B1B linear algebra playlist:

And that will do it for this week’s post. Another short one.

Including Vector Dot and Cross Products, I have three sections left to get through to finish off this unit, Vectors and Spaces. The following two sections are titled Matrices for Solving Systems by Elimination and Null Space and Column Space. In total I have 26 videos left to watch in this unit. Including today, there are ten days left in July so I might be able to get through the unit by August, but I doubt it. I’m going to make that my goal, however, and try to grind through as much as possible this coming week to set myself up well to finish it off next week! It also just dawned on me that I have five weeks left to go before finishing off my fifth year working on KA… Crazy to think about. I never imagined myself saying this but sixth year, here I come! 😳