I can't help but it feels so unnatural to me to learn solutions to problems you don't know even exist first and learn about the problems later, instead of presenting the problems first and then "discover" the solution. Like this null space. It came out of the blue for no apparent reason and then in the end we learn it has some important applications we will learn about later. This way I can't attach any meaning/use to this construct. I understand it at the moment, but it will be gone tomorrow. I don't mean to sound negative but I think this is how most human brains work. I appreciate the effort, and enthusiasm though. That's the thing that keeps me alert while watching this.
Hi Filifow, I agree with you 100%. I think you may have seen this video out of sequence. The first video in "Chapter 6" explains why this concept is crucial: ruclips.net/video/7siCweBXxCo/видео.html Pavel
07:28 "every set of vectors gives birth to a subspace of R4...". Isn't the dimension of R decided by the number of decomposition vectors? How can it be 4 everytime?
An interesting approach. Rank-Nullity is apparent from the FOUR 'domain' vectors *a*, *b*, *c* and *d* producing TWO null-space vectors -what we would expect - since the 'range' of these vectors is itself two dimensional (namely the plane of the blackboard)
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oh my god. talk about a aha! moment. I have never understood why you can multiply/add equations, but I think I get it now!
Thank you for letting me know! It means a lot.
Very clear, thank you for the video.
I can't help but it feels so unnatural to me to learn solutions to problems you don't know even exist first and learn about the problems later, instead of presenting the problems first and then "discover" the solution. Like this null space. It came out of the blue for no apparent reason and then in the end we learn it has some important applications we will learn about later. This way I can't attach any meaning/use to this construct. I understand it at the moment, but it will be gone tomorrow. I don't mean to sound negative but I think this is how most human brains work. I appreciate the effort, and enthusiasm though. That's the thing that keeps me alert while watching this.
Hi Filifow,
I agree with you 100%. I think you may have seen this video out of sequence. The first video in "Chapter 6" explains why this concept is crucial: ruclips.net/video/7siCweBXxCo/видео.html
Pavel
07:28 "every set of vectors gives birth to a subspace of R4...". Isn't the dimension of R decided by the number of decomposition vectors? How can it be 4 everytime?
That was exactly the question I had when I listened to this lecture. I guess he could've said "Rn, where n in this example is 4".
It is a *sub*space of ℝ⁴
It is a *sub*space of ℝ⁴
An interesting approach. Rank-Nullity is apparent from the FOUR 'domain' vectors *a*, *b*, *c* and *d* producing TWO null-space vectors -what we would expect - since the 'range' of these vectors is itself two dimensional (namely the plane of the blackboard)
Right. It's wonderful how linear algebra is ultimately a science of simple counts.