Calculating dimension and basis of range and kernel
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- Опубліковано 19 лип 2019
- German version here: • Dimension und Basis vo...
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Here, I explain the typical calculation scheme for getting dimension and basis for the image/range and nullspace/kernel for a given matrix.
I hope that this helps students, pupils and others.
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
Best video tackling image and kernel, thank you a lot!
Thank you for saving my educational life!
How have your studies been going?
@@PunmasterSTP I changed subjects lol, Literature seems to be more my thing, but thanks for asking!
@@butterflyfilms939 You're most welcome, and I always enjoy the conversation! I've made a lot of changes myself, and I'm glad you found something you enjoy.
This video was so helpful!! Thank you
Thank you! You are very welcome!
The first part of explanation is awesome.
But I didn't understand the range part well since it includes some theory part.
I hope in the next video I could understand more about range
This was helpful, thank you. My professor prefers to not give us simple tips like this for some odd reason.
My professor too :((?. Thankyou for your videos 💜
@@Ucrit_garden How have both of your studies been going?
Basis of range and kernel? More like "Beautiful description for all!" Thanks for making such high-quality lectures.
Hello thanks for the video.May I know if we want to obtain Range(A),whether we could use expression Range(A)=Span{[2,4,8]^T,[3,1,7]^T}?
Of course, you can write the range as a span :)
@@brightsideofmaths thanks for reply. I still have one quick question. May I know what is the usage of Range of Matrix?And if there exists one element p from the Range of Matrix A,whether there exists at least one vector s that can build a expression:As=p?Thanks in advance!
@@lancelofjohn6995 Yes, the range tells you if the system A s = p is solvable at all.
Great explanation,i have a question for the range,you just need to take 2 linearly independent vectors doesnt matter which duo in this case,you took 1st and 3rd,but u can take 2nd and 4th for the range T basis , as they are independent too right?I guess yes.
You have to take two that span the whole range. In the end, it does not matter but it is also better to have a system which ones you can choose.
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@Ethan Maximus You are welcome :)
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When dimension of kernel will be zero and how it can be seen in matrix form??????