Calculating dimension and basis of range and kernel

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)

[@butterflyfilms939]

Thank you for saving my educational life!

[@PunmasterSTP]

How have your studies been going?

[@butterflyfilms939]

@@PunmasterSTP I changed subjects lol, Literature seems to be more my thing, but thanks for asking!

[@PunmasterSTP]

@@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.

[@khaleda.s761]

Best video tackling image and kernel, thank you a lot!

[@PunmasterSTP]

Basis of range and kernel? More like "Beautiful description for all!" Thanks for making such high-quality lectures.

[@shilpar5697]

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

[@fubarace1027]

This was helpful, thank you. My professor prefers to not give us simple tips like this for some odd reason.

[@Ucrit_garden]

My professor too :((?. Thankyou for your videos 💜

[@PunmasterSTP]

@@Ucrit_garden How have both of your studies been going?

[@christopherandrewmartin494]

This video was so helpful!! Thank you

[@brightsideofmaths]

Thank you! You are very welcome!

[@mubasharmushtaq4108]

When dimension of kernel will be zero and how it can be seen in matrix form??????

[@deyvidpopov2778]

This guy hacks the math.

[@horemopik2152]

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.

[@brightsideofmaths]

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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[@ethanmaximus8050]

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[@calvinjoziah8788]

@Ethan Maximus You are welcome :)

[@lancelofjohn6995]

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}?

[@brightsideofmaths]

Of course, you can write the range as a span :)

[@lancelofjohn6995]

@@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!

[@brightsideofmaths]

@@lancelofjohn6995 Yes, the range tells you if the system A s = p is solvable at all.