Find Null Space and Nullity of a Matrix | Linear Algebra

We find as basis for the null space, and the nullity, of a matrix. #linearalgebra #matrices
Find Rank of a Matrix: • How to Find the Rank o...
Finding Basis for the Row Space of a Matrix: • Finding Basis for the ...
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[@WrathofMath]

Help me produce this course by joining Wrath of Math to access exclusive and early linear algebra videos, plus lecture notes at the premium tier!
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[@PunmasterSTP]

When I first took a linear algebra class, I think it was around the time we got to the null space that I started to get rather confused. Thanks for putting together these lectures to help us learn (and re-learn) the material and clear up our misunderstandings!

[@advitranawade3039]

Detailed, to-the-point videos in a modern reaction vid type format? Super creative!

[@WrathofMath]

Thank you!

[@btsloveclub]

took me just a few mins to digest the concept and now i feel confident, most thanks to you!!

[@WrathofMath]

Awesome! Thanks for watching!

[@Snigkar]

deeply appreciate your efforts. step by step thorough explanation helps understand the concept well. thank you so much😊 (by this point, i wish all my math syllabus had videos by you)

[@WrathofMath]

So glad to help - thanks for watching! I hope to have full playlists on all undergrad math courses in due time!

[@user-uh5jo4zb4t]

I have an exam tm.You’re videos are a life saver.

[@WrathofMath]

Good luck!

[@PunmasterSTP]

How'd your exam go?

[@TheThreeMusketeers09]

You explain linear algebra a million times better than my professor, thanks man!

[@WrathofMath]

Happy to help!

[@user-lp2uy5fz3h]

It's very informative for my exams, thanks man

[@WrathofMath]

Glad to help, thanks for watching and good luck!

[@RyantheCanuckpirate]

What a lovely video. There's a smooth progression from step to step without our time being wasted

[@WrathofMath]

Thank you!

[@Bedoroski]

You may not the almight professor that masters every subject, but I appreciate such effort dedicated into explaining it so smoothly. Please keep it up

[@a_mysterious_creature]

Nullspace was melting my brain. Thank you so much!

[@existentialrap521]

Looking good, bro. Good review. Doing some statistics theory proofs and oof they rely hard on this stuff. Thanks!

[@WrathofMath]

Glad to help - good luck!

[@joonk2]

appreciate so much! i had hard time to understand AX = 0, luckily i found this precious lecture so that makes me go to next step! thank you again for sharing this wonderful video.

[@WrathofMath]

Glad it helped!

[@phymadori545]

Super clear explanation from the definition to how to do it. Thank you.

[@WrathofMath]

Glad it was clear, thanks for watching!

[@bat_man1089]

please make videos on limits and continuity in matric space also on their properties

[@SzTz100]

So kind of you to do these very educational videos, thank you.

[@WrathofMath]

Thank you!

[@amcraft2031]

Great explanation! Now I feel a bit more secure in my math exam tomorrow!

[@WrathofMath]

Glad it helped!

[@PunmasterSTP]

How'd the rest of your linear algebra class go?

[@henrywoo1668]

Thank you Sir for your great video . Your explanation is very clear !😀

[@thenewdimension9832]

Thank-you so much you helped me in real analysis and now here also ❤❤❤❤❤❤❤❤
May God bless you !

[@aryanshrajsaxena6961]

Leading variables correspond to those positions which appear first in the reduced row echelon form

[@user-fy3bp1vo6q]

thank you, your explanation is very clear, and this video is very helpfull, all your videos are great

[@WrathofMath]

Thanks so much!

[@agm8554]

That helped out a lot! Thanks!

[@chyldstudios]

well done.

[@Melixmn]

Wow,awesome thank you

[@WrathofMath]

Glad to help, thanks for watching!

[@successorof68]

Are you ever planning to do advanced linear algebra course? These videos are nice to review some concepts but would be better if you are able to do more rigorous L.A. concepts.

[@WrathofMath]

I would like to, but need to make more basic videos first that are relevant to more people to pay for the production of those more niche courses. As soon as a lot of my basic videos break into the pre-algebra search rankings, I’ll be able to make a lot more advanced stuff!

[@successorof68]

@@WrathofMath I understand. Good luck!

[@fortyung]

Is it safe to say that the number of free variables is the null space?

[@atulsomkuwar5671]

i am not understood how 1st roe elements changed if i am going proper echelon form your matrix is differnt than me also i amnot getting last row last element is not getting zero

[@thenewdimension9832]

If possible please make Playlist separately ,will be helpful to find videos 😊

[@WrathofMath]

Do you mean a linear algebra playlist? I already have one, it is linked in the description. However it is currently unlisted - meaning you can only access it with the link. This is just because it’s very small right now, and I don’t want to clutter my playlist space with small playlists, but it will be in the description for all my Lin alg videos, and will be public when it has more content! Let me know if you have any topic requests and thanks a lot for watching!

[@ProgressiveVoice]

Great vid much thanks!

[@WrathofMath]

Glad to help, thanks for watching! Much more linear algebra on the way!

[@bethusilegamedze946]

When you were forming the equation, X2 was Zero(0x2) but now in the matrix it is one(x2), how?

[@WrathofMath]

I'm not sure what you mean, do you have a timestamp/can you be more specific?

[@kunraiyan]

3:57 why write x2,x4 andx5 and not leave them as 0, in accordance with the equations above (in blue)?

[@WrathofMath]

When we solved for the leading variables in the preceding step we found restrictions on x1 and x3. We found no restrictions on x2, x4, and x5. So when I consider the column vector [ x1, x2, x3, x4, x5 ], what is x1? Well, from our work we found x1 = 2x2 + x4 - 3x5. What about x2? Well, x2 has no restriction, so all we can say is x2=x2. If we had found x2=0, we would have written that, but we found no restriction on x2 nor the other free variables x4 and x5. Does that help?

[@kunraiyan]

@@WrathofMath yes, thank you.

[@dyllislee326]

may i know why x2, x4 and x5 are free variables?

[@forsboynewtec9726]

They don’t have leading 1s, X1 and X2 are not free since they have leading 1s

[@gouravmehta4030]

Appreciated 👌

[@WrathofMath]

Happy to help!

[@angelgray8899]

2 pivots and 5 colums. 5-2= 3

[@AnasA.Ansari]

Does this holds for every example?
Any concept behind your generalization?

[@Beyondfutura]

I think You'r RREF is wrong. Please cionfirm it mine's comes different????🤔🤔🤔🤔🤔🤔🤔

[@xolileposwa4924]

😋😋😋

[@ojk_9446]

made it too complicated useless video

[@brotherdom7661]

so basically Null space is = to how many free spaces (or free variables, doesn't matter how you say it) there are