Nullspace Column Space and Rank

Finding a basis for Nul(A), Col(A), Row(A) and finding rank(A) and the dimension of Nul(A). Includes the rank theorem. Watch this video if you’re cramming for a linear algebra exam and want to see the major concepts at once!
Check out my Matrix Algebra playlist: • Matrix Algebra
Subscribe to my channel: / @drpeyam

[@blackpenredpen]

Thanks, I am taking my linear algebra exam within an hour. I don’t want to say this video is helpful, but this video is super helpful!

[@drpeyam]

Hahaha

[@wkingston1248]

I hope you already passed your LA exam years ago lol.

[@ssdd9911]

i m surprised that u could find time to take linear algebra despite ur busy schedule

[@awesomecodeyay8382]

wait, I thought you were a university professor? Why are you taking Linear Algebra ??

[@Apuryo]

I actually have the exam in three hours 💀

[@davidc.7305]

There's no greater feeling than clicking on a video and having all your doubts and questions washed away in one sitting. Thank you, this was extremely helpful!

[@laxmanbafna3127]

exactly

[@Sand7Clipper]

"every answer in linear algebra is row reduction"
Exactly what I was thinking! Thank you sir for making cramming fun and effective 👏

[@nantech431]

There's no greater feeling than clicking on a video and having all your doubts and questions washed away in one sitting. Thank you, this was extremely helpful!
Thank you sir!

[@drpeyam]

Happy to help!

[@ThinkDifferentlier]

meat(A) + fat(A) = steak(A)

[@picnicbros]

Thank you so much! This video cleared the confusing I was having. My professor just threw the formula for rank nullity theorem and I couldnt understand why it was like that. This video explained it nicely and added a gag to it too. Wish I had you as my professor!

[@coolpopk]

Thanks for posting this! I have a linear algebra final next week and I was stressing over this topic. Thank you!

[@cemcalsar3112]

I am watching this again and again.It is masterpiece,you explained everything in 20 munite that my prof. couldnt explain to me in 3 weeks.Thank you so much,Sir

[@cemcalsar3112]

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I actually do have an linear algebra exam in an hour and needed this video so badly !

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[@abdulnafayazam3213]

What a top G. Huge respect for you brother

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Thank you so much, sir! You clarified my confusion hell out of me!

[@mohammedal-haddad2652]

I liked the M and N acronyms rule. Thank you very much for this lecture.

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Your way of teaching is so good👍

[@AbramFontanilla]

Amazing video. Thank you!

[@faridbabayev1657]

THANK YOU SO MUCH! God bless you sir!

[@hofstra7591]

Wow, thanks for the video, your explanations helped me a lot.

[@luiavalos92]

Wonderful video Professor.

[@nerodant85]

Thank you for the video Dr. Peyam

[@FarhanObaid-cl7yt]

Brilliant!! Absolutely Brilliant!

[@pinkkitty6553]

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[@Jessi-lw3iw]

Thanks for the amazing video ! I found hope in linear algebra again !

[@drpeyam]

You are welcome!

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Thank you for this video!

[@mnstrnmocutsy5441]

u make maths so interesting. thanks Sir. it was so clear

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You are so sweet...
You explained very easily, the most confusing topic for me in linear algebra.

[@mauricioconlaparva]

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[@Memes_uploader]

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[@mariamacamaraderie2613]

thank you so much, this was an eye opener.

[@QuantumByt3s]

You are a fantastic teacher :)

[@laxmanbafna3127]

So helpful sir. Thank you so much

[@nonnamoon5960]

Thank you for this video😄This video make me pass the exam in linear algebra 😄I like it

[@Tkc__]

Bro you’re too good at teaching this concept… I’m crystal clear now, thx a lot!

[@drpeyam]

Thank you :3

[@wiz1537]

What a life saver! I wish i saw this video earlier,, I have my la exam tomorrow and i was still having hard time understanding all those concepts,, and this single video untangled everything in my brain:) You r not even explaining in my mother tongue but you got me better than my own professor who speaks the same language as me hahaha
Thank u so much!!!!

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[@benhigh9302]

well done and thank you. extremely clear information and process

[@drpeyam]

Thank you!!!

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thank you sir...its really helpful 😊

[@tomasgoncalves6736]

Thank you very much for the video!

[@neeldesai501]

super informative thank you!!

[@Helena-vb7mw]

Thanks! explaining everything in very simple way

[@drpeyam]

You're welcome!

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Thank you, you are excellent!

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You Made my day ❤

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It's more than super helpful 🙂

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This channel is soo underrated

[@drpeyam]

Thank you!!!

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Ok, This was actually a Great video THANK A lot sir!!!!!

[@pranavgandhi9224]

Amazing sir..... thankyou 👍

[@terminal9229]

I don't know why his way of teaching makes me happy ...Anyways thanks for clear explanation of concepts .

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Great Examples

[@killer4791]

+ Respect
Need more enthusiastic teachers/lecturers/professors like you
May Lord Shiva Bless you.

[@stumerac]

I like how two seemingly parallel lines in this video seem to intersect somewhere off screen to the right. Do the top and bottom of the whiteboard form a basis of the column space of the whiteboard from this angle?

[@mustafaaljumayli6615]

Thank you so much!

[@himanshuraj5837]

hey sir thanks a lot you cleared any of my doubts

[@definitelynotty4360]

Thank you!!

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you are a great man

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[@mohamedshahin6177]

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[@drpeyam]

You’re welcome!

[@deepikasharma7736]

Thank you so much sir

[@huyvodeptrai]

Thank you

[@naturelover82003]

lot of thanks🥰🥰

[@user-bu8mg7uq3s]

thank you

[@amardexter9966]

If you imagine 2x1 matrix, the transformation takes 2D space to 1D space, meaning there exists a line in the 2D space that goes to origin after the transformation, meaning that it's the null space of the matrix. Since column space is the output span, and null space is in a sense number of dimensions lost, the N (original number of dimensions) becomes the sum of column space and null space.

[@nihalsahil9074]

Thanks sir

[@Smoothcurveup52]

Thanku sir

[@ahmad-jd7nh]

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[@briankichini7380]

yea the video is super super good

[@drpeyam]

Thanks so much!

[@SauravKumar-12354]

sir , why didnt you wrote the simplified matrix in row space span ? u said it preserves the span .

[@SmileyHuN]

Awww we just learned rank recently, vector system's rank, rank of a linear function and ofc matrix rank. Also the Kronecker rank theorem and so on ^_^

[@XanderGouws]

4:17 - since those are 3 linearly independant vectors in R³, their span should be all of R³, so wouldn't the columns of the identity matrix also serve as a sufficient basis?

[@XanderGouws]

Or any other set of 3 independant vectors

[@drpeyam]

Yes, of course!

[@LuisBorja1981]

@@drpeyam and what about the 3 L.I. vectors of the row-reduced matrix? Shouldn't they span R3 as well? I didn't understand the "span non-preservation property" between the L.I. vectors in the original matrix vs the L.I. vectors in the row-reduced matrix

[@nicolasrios7198]

Dr. Peyam should get waves 🌊

[@fadibenzaima5348]

Is there any video that explains these concepts and why row reduction works geometrically ?

[@drpeyam]

You can check out the playlist!!

[@glennxhose7217]

Tell you what. This video saved my test 2😂. Took something of 2 weeks into 20 minutes 😂

[@Big123456Boi]

wow this helped alot!!

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I bet that when you play Super Smash Bros, you always go for linear combos.
These are the best ones :P

[@drpeyam]

Hahaha, of course 😂

[@MittaManishGupta-de1xb]

How are you teaching sooo good sir

[@drpeyam]

Awwwww thank you!!!

[@yousefmayeli7584]

First thanks it was very useful second I got headache for camera’s angle

[@mardzj]

4:04 Row reduction destroys span? Why, columns 1, 3 and 5 are Linear independent and span R3 just like before row reduction
Is the span of the matrix all 5 columns?

[@drpeyam]

Yeah but this example is just a coincidence

[@lucasmoro8775]

valeu paee

[@macywallace7904]

when you are finding the Col(A) can you use the RREF or do you have to use REF

[@drpeyam]

REF is enough

[@macywallace7904]

@@drpeyam but can you do rref and the answer be the same?

[@drpeyam]

Yes, since the pivots are still at the same positions

[@sarimshafiq8826]

I was watching etc etc n etc then found it now I regret why didn't I found it earlier.

[@insert_a_good_name_here4585]

Heck, within 30 seconds I feel so called out lol

[@holys6348]

for the colspace of A. I think you needed to out "span" of such 3 vectors

[@joynanjero6236]

The negative nine and positive two... Shouldn't that be positive nine ? Kindly inquiring

[@drpeyam]

I think so, see comments

[@sharifahmed45]

Thanks Dr Peyam, is there anyway you and your team will do a real analysis for those struggling in undergrad schools and introductions of proofs. Thanks as always, and it is a pleasure to watch your output.

[@drpeyam]

Real Analysis czcams.com/play/PLJb1qAQIrmmDs56gwp6yeytyy0wxWLac8.html

[@mashnoonmayad]

how does -7 act as a pivot? Doesn't it need to be 1 to be a pivot?

[@drpeyam]

No pivots can be not equal to 1

[@toughconstruction5044]

RoWs and nOse

[@drpeyam]

Columns Schmolumns 😂

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Bro he is hacker 😮 🔥

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“maybe you have an exam in an hour”
Me: 😳 he caught me

[@kr4156]

00:13 I have the exam in an hour 😂😂

[@somnathkoley7317]

Row space and column space be like: I am inevitable.
Dr peyam: and I am......🤏 🤏Dr peyam.
Thanks for helping me sir.

[@SheeNdegwa-lw4nr]

I have exactly one hour 2 minutes to take my linear algebra exam 😭