Not bad, I understood all of it. I've seen different proofs that expect the reader to assume things, but yours contains only elementary elements that are not complicated.
The definition of an elementary matrix is a square matrix that has exactly one row operation done to it. Check out the following video. ua-cam.com/video/7H3JFH3IjB0/v-deo.html&ab_channel=Mathispower4u
Great video! I just had a question, at 23:54 when you expanded the determinant of B on column 1, where exactly did that expansion come from? Is that just something we're assuming to be true?
Question: where did that i + 1 come from at 23:58? Edit: I mean apart from the fact that it comes from the general formula which says i + j and j happens to = 1.
The definition of the determinant that I am using has that formula as a definition. It's from that definition that I am trying to get to the i + j formula.
15:00 In previous video, You use cofactor expansion on any rows to prove that the swap operation get negative det(A), but in this video, you use this Theorem to prove cofactor expansion along any rows. It feels like an egg and a chicken problem😢
This video is independent of my other Linear Algebra videos. In fact, I don't require it of my students. I simply put it out as a complete video all its own. So, do not use the definition I used in previous videos. In this video, the definition of the determinant was defined to be along the first column. Thus, when I try to prove the theorem along any column, you can roll the columns until you get to the first one, and then you can use the theorem. Once again, DO NOT USE any other video of mine - this video is completely self-contained.
Not bad, I understood all of it. I've seen different proofs that expect the reader to assume things, but yours contains only elementary elements that are not complicated.
great video! Greetings from Norway :)
Thank you very much!
Where can I find the definition of elementary matrix?
The definition of an elementary matrix is a square matrix that has exactly one row operation done to it. Check out the following video.
ua-cam.com/video/7H3JFH3IjB0/v-deo.html&ab_channel=Mathispower4u
Great video! I just had a question, at 23:54 when you expanded the determinant of B on column 1, where exactly did that expansion come from? Is that just something we're assuming to be true?
Yeah, in this video I assume the definition of the determinant along the first column.
Yah, the same question with you. It's really confusing. Hopely he will explain it more clearly.
@@nguyenjohn1649 At the very beginning of the video is the definition that I am working with.
Question: where did that i + 1 come from at 23:58?
Edit: I mean apart from the fact that it comes from the general formula which says i + j and j happens to = 1.
The definition of the determinant that I am using has that formula as a definition. It's from that definition that I am trying to get to the i + j formula.
15:00 In previous video, You use cofactor expansion on any rows to prove that the swap operation get negative det(A), but in this video, you use this Theorem to prove cofactor expansion along any rows. It feels like an egg and a chicken problem😢
How do I fully know how to prove this theorem properly😢😢😢😢
This video is independent of my other Linear Algebra videos. In fact, I don't require it of my students. I simply put it out as a complete video all its own.
So, do not use the definition I used in previous videos. In this video, the definition of the determinant was defined to be along the first column. Thus, when I try to prove the theorem along any column, you can roll the columns until you get to the first one, and then you can use the theorem.
Once again, DO NOT USE any other video of mine - this video is completely self-contained.