Yesterday I posted the final worked-out exercise from chapter 1 of Gilbert Strang’s Linear Algebra and Its Applications, Third Edition. My first post was for exercise 1.2.2 almost exact 15 months ago. The book has eight chapters and two appendices, all with associated exercises, so based on my track record thus far I’ll finish the book in 150 months total or over 11 years from now. However more recently I’ve picked up the pace considerably and have maintained a pace of posting one exercise per day. At one point I estimated that the book contained 700-800 exercises, so even at that rate it will still take almost three years to complete unless I can post more rapidly.
However I think this project is worth doing, as (re)working through the exercises for the posts has considerably improved my understanding of the material. There were several articles where I had typos in my first attempts, I did only partial proofs (for example, showing a matrix was a right inverse while forgetting to show it was a left inverse, or I just didn’t understand how to work the exercise.
Most notably, the very first time I tried to work exercise 1.4.24 (on paper) I didn’t understand at all how multiplication of block matrices was supposed to work. Even when I worked it out again and did my post on exercise 1.4.24 I got the right answer without fully understanding why it was right. This lack of understanding also showed up in working the final part of exercise 1.6.10. and motivated me to stop working on further exercises until I proved for myself how multiplication of block matrices worked.
That in turn led me to look at various questions about diagonal block matrices, including how to define them, how to multiply them, and how and when you can find their inverses. In the course of investigating those questions I went some way beyond what I needed to show in order to work the Chapter 1 exercises, but I did get a good basic understanding of block matrices in general and diagonal block matrices in particular, one that I think will be useful in future. (This also produced some minor refinements to my thoughts about multiplying block matrices and led me to update my original post.)
No rest for the weary: My next post will be tomorrow, for the first exercise of chapter 2.