Just FYI for people watching his work at 7:23, it's supposed to be 5 7 3, not 5 8 2. Main takeaway from this video is that determinants by column are calculated exactly like determinants for rows. Thanks for the video!
Hello Professor Dr. Grinfeld; First I definitely must thank you for your teaching, which is very beautiful and the most appropriate for future mathematicians. As in college as on RU-vid, many professors teach an engineering way If I may say, which doesn't include proofs, paths of reasoning and critical thinking. Is more about applications, solving exercises and very connected to the real world. I've already finished Linear Algebra 2 playlist. I've actually learned math for once. Your map of the determinants was just beautiful art and using a laser? Can't describe using other words than elegant, beautiful and logical. Now I would like to learn calculus for now. Do you have any calculus playlist for begginers as the linear algebra ones? I went to lemma, but only found a video about it which isn't you :( Thank you very much
Thank you so much for making these videos. They have been a great help to me, and I imagine to many others. Could I ask you to take a look at the "5 8 2" entry at 7:23 and see if you are happy with it? I expected it to be "5 7 3". In this case, the whole matrix is multiplied by 0 so it doesn't affect the result. I hate to be the nit-picker but I thought you might want to check it out. It is always possible that I misunderstand some aspect of the calculation, of course, and perhaps you got it right all along.
Thank you Pavel, I am glad I've found you. I've gotten this far from the very beginning of the series in a week or so :) I still can't understand one thing about determinants. Why doesn't it make sense in principle to try and define a determinant for non-square matrices? Have you already explained that anywhere in your videos?
There are analogous definitions, but none that yields a single number. The determinant is a measure of the change in "volume" under a linear transformation. But if dimensions are mismatched, the comparison doesn't work.
It follows from the general algebraic definition ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-D8rghkxf4eUz.htmlz Think about what is left when you factor out one of the terms.
