How to find the null space and the nullity of a matrix: Example

In this video, I will walk you through an example where we find the null space and the nullity of a matrix. The null space is expressed as the span of a basis.

[@streetwolfe]

R.I.P. my ears

[@nathanweems4952]

R.I.P. my ears, but still very helpful

[@jamesfreefoot]

scared me

[@ekramabdull6743]

😂😂😂

[@harshraj-wd2rr]

😂😂 me to also

[@pexilated1638]

Oh hey cool a video so I can freshen up on some concepts lets watch.
“HERES AN EXAMPLE OF HOW TO FIND-“
“.....ow”

[@luiscorona552]

RIP Headphone users

[@erwinjedracho640]

this is by far the most clear and shortest explanation of the subject

[@vanadium4603]

instead of taking my linear algebra final, i had to spend 3 months in the hospital after getting my eardrums blown out. thanks joy zhou.

[@__Pat]

Great explanation. Worst mic of all time LOL.

[@joyzhou4917]

Haha, agreed, sorry about the mic!

[@Alex-dn7fd]

Simple, fast and loud. I like it

[@kevinlin4157]

Love the explanation, it is crystal clear how the nullity of a matrix works and finding the null space. Thank you very much.

[@aniketchoudhary729]

Finally I found a single understanding video for null space.....

[@sanchitkumar9050]

This was the most easy to understand example present on youtube. Thank you so much

[@yadusolparterre]

Finally someone who can explain it fast and simple !

[@HarikrishnaRao]

Thank you, Joy Zhou. Great explanation!!! You literally saved me.

[@nathanwong3900]

Thank you! That was so helpful! Also, great handwriting!

[@harshagupta1707]

This kind of short videos are saviors!

[@sasanfouladi-pour4691]

Really helpful, and way clearer than my University of Glasgow lecturer...

[@ARNAKLDO]

I really like how you broke down the definition step by step. UT was clear and understandable. Thank you!

[@muhammadfaisal5965]

Awsome brief and comprehensive explaination.

[@rafaelsantana616]

great video. the best I'ven seen about this subject.

[@yogeshbhurtel1865]

i have an exam today thanks 😉

[@alpha-mf9rh]

This was quick and easy to understand .Thanks

[@Omkar-ku9to]

easy peasy
thank you for this explanation

[@mography4563]

OMG thank you thank you soooooooooo much for an easy solution. God bless you!!!

[@aibdraco01]

Girl !!! You saved my life!!!! Thanks!!!

[@Kicsa]

This is a great video, thank you!

[@RightInTheMiddle]

Best explanation ever thank you sooooo much!!

[@gekongachacha]

Thank you for a good explanation.

[@bobolecoq2599]

pretty straightforward. thanks

[@mahatma2147]

you are great...thanks for this video❤️❤️

[@sfundoy5dube59]

Thank you ma'am your great work is much appreciated

[@kronax6043]

Thank you base boosted math teacher

[@BadarToor]

Very Very Nice Explanation,,, I got it.. thank you so much

[@GeneralGiggleMuffin]

Very helpful. Many thanks.

[@erikh7805]

Hi, professor Joy Zhou, so the last column of (1,2,4,-1) will be ignored when we try to find nullspace? I mean for everything kind of this question, the last column is always omitted?

[@AyeshaAmeen]

that row in the reduced echelon form is all zeros which is why she doesn't end up using it to get equations

[@prateekkumar.1325]

Nice teaching .maam!plz keep uploading more of these.

[@yeakpeak]

Thank you, life saver

[@Alfredo52993]

you are the best, thank you so much

[@robertwilsoniii2048]

This video is fantastic.

[@kaeluvsfortnite]

The nullity is equal to the number of arbitrary variables. Any variable that isn't a leading variable in the echelon form of the augmented matrix. right?

[@assister93]

Great video! Thanks!

[@shahdaybhai9803]

I subscribed your channel,liked your video, pressed bell icon and the reason is your beautiful voice and your pretty hands.:)

[@donzelwashington]

fantastic video, thank you

[@javeedfatima438]

Thank u so much...
Helpful for me..

[@anshikagupta4407]

Thank you, very helpful 😇👍

[@bluebloo5574]

不錯，感謝。

[@thisisshy8177]

Brief & clear

[@motorheadbanger90]

How is this different from finding a basis for A? The procedure seems to be the same

[@tails8491]

영알못이지만 너무 잘 푸셔서 바로 이해했다 ㄷㄷㄷ

[@mathew5880]

And it shall remain forever a mystery what the null space of A was .....xd jk ig it's 2 .but jokes aside this video was really simple and concise and it really helped clear my concepts of nullity thanks alot joy

[@leafierk5565]

i love u pretty handwriting and soooooo clear expression

[@dbsxogh2]

so the number of independent column vectors is nullity of A?

[@fantiscious]

*_"AAAAAAAAAA"_*
"Therefore the nullity of A is two :)"

[@anshumanpratapsingh9150]

What if the element at (0,2) is 1

[@davidcristobal5108]

Amazing thank you.

[@user-ky7jl3gu8k]

The video is old but the concept is taught well

[@HatsyRei]

Thank you! :>

[@keithng51]

Thank you very much

[@phuccoiinkorea3341]

how do you know x1 is independent ?

[@budasfeet]

I think it's by choice.

[@juliorosas-cortes424]

7 years later: thank you ! November 2022!

[@varakumarmathematics1240]

needed some more explanations

[@nihinkcmxhfwnhi]

thank you!

[@lolno6527]

Amazing explanation! Keep making more videos on maths!

[@anahitaroshani1083]

very useful
thanks

[@takeoff984]

wow that was the best explainaation ever but the mic a little bit too loud

[@Rob-J-BJJ]

thank you so muh ms!!

[@NiggaSlayer666]

thank you so much

[@sanskaripatrick7191]

great explanation although mic quality could be better

[@DouglasHPlumb]

well done

[@SitBackAndRelaxPlz]

this is which pencil?

[@EsperanceBG]

thank you:)

[@toddakiva2770]

Thank you

[@kaizeali1415]

Great brief explaination, Thank YOU!

[@dannyramzan3838]

was the mic in ur trachea necessary

[@HK-sw3vi]

beautiful

[@thelastcipher9135]

everything was clear to me until you removed xsub3 and xsub4 to write span. shouldn't xsub3 and xsub4 always be specified?

[@joyzhou4917]

Thanks for the question. In fact, x_3 and x_4 can be any real number. We can't really specify pinpoint the values of x_3 and x_4 because they are free variables. That is why the solution set is the set of all possible linear combinations of two vectors, and therefore the span of those two vectors by definition of the span.

[@benjaminhoey5777]

thank you

[@mayursarade8217]

I love your voice...

[@naumanshafique1745]

thanks.

[@Teagle]

Me *with headphones*: pausing the video after 10 seconds to see if anyone was talking about her mic
Also me: laughing my ass off because all the comments are about her shitty mic.
Just finished and great video btw

[@gary-en3dg]

Thanks

[@DimesCS]

gave me a heart attack at the beginning

[@HappyPotato21]

best tutorial in 2024 EUNE

[@subhashreesahoo2952]

Thanks for good explanation..😇😇

[@PerkingBJ]

ty

[@thefaceofkenyatoday5968]

I like it

[@mmusic.9507]

nice

[@TheFinalStanza94]

was this recorded on a walkie talkie

[@marklvrd]

Really hard to follow for such an easy problem.

[@prateekkumar.1325]

Tysm😍😘

[@Saladon89]

oh ok she went all the way RREF, thought she went only to REF

[@ShootNPissUrSelf]

MY EARS very helpful vid

[@waqaralishah5446]

she could have save our time if she told that in start that dimention of the nullspace is equal to nullity

[@linguafranca7834]

OK good but what about the last!

[@jacksonmorris9234]

8/10, -2 because mic was lodged under tongue

[@Chrome47]

Very helpful video. Audio is quite distorted, on youtube it's sometimes referred to as recorded with a potato or some other object. And the inner english snob wants to correct you saying homo-genius to homo-gen-us. Thanks again :)

[@joyzhou4917]

Haha, thanks for the suggestion.

[@thomaselder4076]

Feel free to count the number of syllables displayed in the dictionary for homogeneous to find out that homo-gen-us is incorrect. Joy's pronunciation is correct. IF you're being a snob anyways. In reality, people say it both ways.

[@oliverbeck6839]

it's spelled homogeneous and the lady pronounces it correctly: Homo-genius. You are wrong and an idiot for thinking that you are above her!

[@ken8844]

I got confuse when you mentioned span and basis.

[@lolno6527]

coz u stupid

[@ken8844]

real mature

[@budasfeet]

the solution x is a set of value that can be represented by two vector with coefficients x3, x4. This set is a vector space, which has those vectors as its unit vectors, or so called basis. A vector space is spanned by vectors, or basis.

[@codercodes7538]

i wanted to focus but all my mind is like focusing on bunch of hair on the left😶‍🌫

[@maxpercer7119]

nice video but don't shout into the mic

[@ateebahmed2237]

nice pencil

[@rbrtsparkman]

this is such a great video! insta-subscribe

[@fahrezadhia]

the only downside is ur mic, but your explanation is more important than your mic. Thank you.
edit : i like your handwriting