My goal is always to study on KA for five hours which I’m not sure if I managed to do this week, but I made some decent progress, nonetheless! I finished the section Vector Dot and Cross Products, then made it through the entire section Matrices for Solving Systems by Elimination (but to be fair, it was only three videos long…), and also started the final section of this unit, Null Space and Column Space. I was pretty confused as to what was going on in the second section, so I also watched a video from a creator on YouTube whose channel’s named Wrath of Math which was very helpful. I probably could/should have got more done this week, but I feel like I gained a lot of clarity on vectors and matrices and understand how they work much better now. Definitely nice to feel some momentum again!

Below are some screen shots from the final video of Vector Dot and Cross Products which go through how to calculate the distance between two planes. One plane’s coordinates are given via the standard plane equation, Ax + By + Cz = D, and the other by stating the coordinates of two lines that fall on the second plane. I somewhat understand why the standard equation for a plane looks and works the way it does, but I have no clue how or why the expressions for lines look the way they do. I can’t explain how Sal got to the solution, but here are some screen shots from that vid:

Even though I didn’t understand how Sal solved this question, I picked up some of useful info insights:

The next section, Matrices for Solving Systems by Elimination, introduced a technique used to solve systems of equations (I think) that was new to me called the Row-Echelon form. I didn’t understand what was going on and Googled it and found the Math of Wrath video that I mentioned. Here are the notes I copied from that video, a few screen shots that show the difference between what’s called reduced row echelon form vs row echelon form, and an example of turning a matrix into row echelon form:

I got back to the KA vids and used the same method to work through Sal’s example in the second video of the Matrices for Solving Systems by Elimination section:

Honestly, I don’t really understand what the solution means. It might be describing a plane where it’s x-, y-, and z- intercepts fall on 5, (–1), and (–1) respectively, but I have no clue.

In the final video of the section, Sal worked through the same type of question and used the row echelon technique to solve it which resulted in the bottom row of the solution’s matrix being [0, 0, 0, 0 | –4]. Apparently what this means is that the vector being described in that row doesn’t intersect with one or maybe all of the other vectors in the matrix. Once again, I don’t know if that’s correct, but that’s how I understand it at this point. Anyways, here’s some screen shots from that vid and the notes I took working through it:

I only managed to watch the first video from the final section of this unit. The main thing it helped me with was simply understanding matrix notation and helping it sink in for me. It went over matrix-matrix multiplication and matrix-vector multiplication and it all became much clearer to me. It also defined the word ‘transpose’ which means to turn a column-vector into a row-vector or vice versa. Here are some screen shots from that vid and my notes:

And that was it for this week. All in all, pretty good! 

I’m officially 11 videos away from finishing off this unit. After that, I’ll have two left to go before I can cross Linear Algebra off the list. Neither unit has any exercises in it, but each have a million videos so I expect they’ll both take me awhile to get through. I’m only three weeks away from hitting the five-year mark, although I’m a bit confused since the start of September is three weeks from now and September was the month I started KA, but it will also be Week 262. But the start of the sixth year should be Week 261…? 🤔 (Right? 52 * 5 = 260, so Week 1 of year six should be 261…? 🤷🏻‍♂️) I won’t make it through LA by the then but hopefully it won’t take me too much longer. Then I’ll only have Differential Equations and the Multivariable Calculus course challenge left to get through and I will officially be finished the Math section of KA! Assuming I get there, this will be me.