220704Mo Solving Multiple Systems, Updated (Now with Audio)

This video recording is prepared for the third day of LinAlg1 in Fall 2022, and is an updated version of a 2021 silent version. It focuses on simultaneous solution of two (2) (2x2) system of equations over the real numbers. There is at least one grammatical error, and at least one "hando" (like a typo, but I did not type it), for students/viewers/readers to try to correct it, and then try their hand at solving and presenting a correct complete solution, i.e., as an exercise for the viewer. The presentation is also meant to help introduce the viewers quickly to notation and terminology, in an implicit manner. For example, the notation "rref(X)" in this video stands for "Reduced Row Echelon Form of the matrix X", and matches the notation used in several fairly useful software packages that can be used to help one learn matrix algebra and to help one apply matrix algebra. More explicit discussion of these things will be the subject of later videos.

Because this is essentially a lecture video, it is a bit long, as compared to many on YouTube that abide by certain "guidelines for online teaching" that seem to suggest that one should only have lectures of five minutes or less. There is much to say here, and it is all important, even if some viewers think it's trivial. The "triviality" is by design, and that design is pedagogical: students need to see the connections in a setting that is easy enough to do the calculations, but difficult enough to show why a very contemplative approach to problem solving in the early part of a course is more than just helpful - it is essential. Later discussions will help elucidate where are the redundancies and how on an exam, one can meet the assessment expectations without including the redundancies here, and still completely, concisely, and correctly explain the solution attempt one has in mind. Thus comments about "why didn't you do it my way; it's faster?" are mostly out of place here. This is a video aimed at instructing students, not at showing experts that I know how to solve this problem in a flash. It's not a race.