Null Space of a Vector Space

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! In this video, I describe what the null space is and also find the null space of a matrix A.

[@ghost4118]

You got me through undergrad and now we’re getting through graduate school. Thank you Patrick!

[@al_sprays_paint8669]

patrickJMT videos are one of the most helpful online math resources I can think of. I'm in college and I still rely on these videos to explain concepts quickly and accurately.

[@patrickjmt]

thanks! :)

[@sgifford1000]

I'm 66 and just now figuring this out. Wish I had the internet back in '73. Thanks Patrick!

[@patrickjmt]

happy to help! if it makes you feel better , i didn't have videos when i was in college either!

[@Saaad2]

Never gave attention to my calculus and linear algebra instructors because I know parickJMT is there for me. Bundle of thanks..

[@maxpercer7119]

i dont think he would be happy to hear that

[@jacobdavis6743]

Dude I’ve been watching for years now since Uni Phys I. I can’t tell you how much your videos help. I hope you teach classes IRL, the world needs more teachers like you!

[@alakamyok1261]

you are clearly teaching better than university lecturers in my scholl

[@mohamederguig4624]

the best Tutor ever

[@patrickjmt]

thanks! :)

[@Pikrip]

It's 11:56 pm and i have a linear algebra test tomorrow lol! Glad i noticed this video

[@Pikrip]

Thanks for that, Patrick!

[@patrickjmt]

you must be in europe or africa :) good luck on your exam! :)

[@Anubis10110]

you are not alone..i'm here with you :)

[@lianahasan3762]

its creepy how accurate this comment is

[@JCatharsis]

Hey Patrick, words can't describe how much I am thankful for your math series. I literally grew up with your videos since high school and up until now in undergrad. I will definitely support you on Patreon as soon as I get a job haha. Thank you Patrick!!!!!!!!

[@kedah2398]

Pat JMT got me through my undergrad engineering math courses way back when. Now I'm back doing my Masters many years later and BAM... Patrick JMT!! 😁😉

[@ylvaeriksson5761]

You have your favorite educators. First my was NancyPi, but she disappeared. Lucky for me you are still here. :) Thank you!

[@drizzy8450]

Thanks Patrick, you make my academic life much easier!

[@HassaanALal]

You are at the moment, world's best math skilled guy and tutor to be honest.

[@SpaceJesus25]

at the moment.

[@tracywang2677]

your teaching is much more understandable than our lecturer

[@changlinlei7600]

I have 97 in linear algebra so far just by watching his videos and not attending class because my teacher doesn't explain well

[@pedrodelfino9493]

I missed this video, your channel is great! Please complete all the linear algebra stuff =)

[@davidjones5319]

Quite excellent. Thank you for this video. I’ve understood the geometry of the null space, but not understood the algebraic relationship. Thank you for working from start to finish, and then explaining the final relationship to the original system of equations.

[@anshumansahoo8344]

best video on null space i have seen so far

[@kennethhowell5291]

Thank you for your help! The best!

[@patrickjmt]

thanks man!

[@hashbrowncookie8444]

Can't believe I used to watch your videos for college, and these same are going to make me pass for unergraduate level hahaha.

[@landenjones7659]

Have been struggling finding the null space all semester. Thanks for sharing!

[@mathlab1639]

I have been watching your videos to get through my linear algebra course. your videos have been so helpful. Plz do a video on orthogonal and orthonornal systems. Thanks

[@RoninCunningham]

best math teacher since grade 11. Now in 2nd year. Still the best

[@shilpamishra3817]

Wow!! Awesome tutorial!! Greatly enjoyed!👍

[@maxpercer7119]

We can also show that the nullspace of a given matrix is a subspace. Henceforth assume the given matrix, call it A, has size m x n. Let us define the nullspace of A, denoted by nul(A), as the set { x_n : A*x_n = 0_m }, where x_n is a vector in R^n, and 0_m is the zero vector in R^m. In words the nullspace of A is the set of all solutions to the matrix equation A*x = 0. Claim : The nullspace of A is a subspace of R^n. Proof: To show nul(A) is a subspace of R^n we need to show the zero vector 0_n is in nul(A), and nul(A) is closed under addition and scalar multiplication. Sub-claim: nul(A) contains the zero vector 0_n. Sub proof: A * 0_n = 0_m. Therefore by definition 0_n is in nul(A). Sub-claim: nul(A) is closed under addition. Sub-proof: Suppose x1_n , x2_n are in nul A. Then by properties of matrix multiplication we have A * (x1_n + x2_n) = A * x1_n + A * x2_n = 0_m + 0_m = 0_m. Therefore x1_n + x2_n are in nul(A). Sub-claim: nul(A) is closed under scalar multiplication. Sub-proof: Suppose x_n is in nul(A) and c is in R. Then by properties of matrix multiplication A (c*x_n) = c * (A * x_n) = c * 0_m = 0_m. Therefore c*x_n is in nul(A). QED.

[@comedian2479]

Thank you for actually showing examples!

[@sai226]

Its the 3rd semester and another math final and here comes @patrickJMT to rescue me once again

[@nikhilfromyoutube]

Thanks patrik! This video helps alot, can't forget again! One request to upload a video on orthogonal and orthonormal inner product space... this may getting sometimes confusing... I hope you do it!

[@PatrickLoobs]

Thank you! You explained it very well!

[@retrospades39]

And here I was thinking Sonic Team was being creative. But, I guess they went on KZbin and decided to type up Vector and Space together like they actually matched.

[@Anubis10110]

Thank you so much, you are a life savior ... Thank you so much

[@lian3911]

thank u so much im gonna pass my test bc of u

[@user-rb4bv8st5q]

thank you so much you saved my life again

[@joelpalkia]

im loving this! linear algebra ftw

[@IshaqKhan-rk5bl]

U R BEST OF THE BEST TEACHER THANKSSSSSSSSSSSSSSSSSSSSSS

[@SS-605]

Hi Professor, Can you please upload some videos related to the proof that: R(A^T) and N(A) are mutually orthogonal subspaces. (where R represents Range of matrix )

[@shilpamishra3817]

Nice tutorial!!👌 Thank You ~

[@morgano7535]

You're a life saver!

[@EccoMath]

PatrickJMT is really fantastic and all in all this video is good, but the title is very misleading. It is valid to ask for the Null Space of a Matrix. It is valid to ask for the Null Space of a Linear Transformation. But it is not valid to ask for the Null Space of a Vector Space, as the title suggests. A vector space is just a set of vectors; it doesn't send inputs to outputs in any way, so you can't ask which vectors are being sent to zero by the vector space.

[@tessacarstairs5998]

This is wonderful

[@joacocrabtime1032]

You either: 1. Study null space, or... *DOUBLE BOOST*

[@Prauwer]

Easy way to solve that problem

[@MarjanAmbroze]

*TOGETHER WE CAN SHOW THE WORLD WHAT WE CAN DO*

[@yashbhat-xia3962]

helpful, thanks bro!

[@connortmurphy]

Awesome! Could you do a video on row space and column space?

[@ramazanaktas3699]

I have a question. What if we have a zero vector within A? I.e. one or several variables vanishes after we write Ax in equation form. Let's assume we have second column of A(lets say it is 3x4) consists of zeros. Do we add that variable to the Null(A) as x2[0 1 0 0] transposed?

[@miketheguy2847]

I AM NOT WEAK!

[@jaymur001]

This would have been so helpful two semesters ago.

[@user-lk2el1fz6r]

thank you sir.

[@brianmoreno3222]

Do you have something for a high school student of precalculus who need help with trigonometric identities? Specifically verifying and simplifying

[@user-xz9st8hm1n]

saving me as always

[@squiintts]

Thank you!

[@skatelife59]

Is it correct to say, null(A) = span{those two vectors with alpha and beta}

[@kristel8859]

hey patrick will you please make a video about Fourier series and transform. Im having a hard time understanding it. thank you

[@patrickjmt]

i already have

[@alen7648]

What is the difference between finding a Kernel of A and finding the Nullspace of A? :) It seems for me to be the same.

[@lawrencekamya2399]

Is null space the same as nullity of a vector space??

[@makemarshall7041]

Thank you

[@Lifebeam87]

what is the basis of the nullspace?

[@manuelaidos]

with the vectors of the nullspace you found you can do a row reduction with them and find if they are basis or not simple

[@michimellyqichen7691]

Hi, is there any video for row space and column space ?

[@patrickjmt]

no, i don't think i have made one for that

[@natalioramirez6240]

in what playlist can I find the other videos

[@vidhucatherineantony]

What is the difference between null space and span ?

[@chilidog2469]

I have no clue what this is, and I'm still doing algebra

[@AbhaySingh-fd4ds]

i'm having trouble finding your all vid on laplace transform in order in the playlist i found them but, they are not all vids somebody please help me😣😣😣

[@mechanwhal6590]

All the normal people will be so confused when they look at the comments.

[@eylmaz6696]

is kernel and null space same?

[@john2526]

My mom will never believe that i am using KZbin to study math...however, neither am i..

[@GeoDasher8]

I thought this was sonic

[@gea7449]

Sonic null space

[@Muse-mz4hb]

Is null space the same as a kernal?

[@xXBR4D3NXx]

yes

[@SteelersFans99]

Patrick make a Patreon!!

[@patrickjmt]

i have! go forth and donate! :)

[@hyperprimetime]

Dooble boost null space

[@emotional7332]

patrick are u planning to make geometry videos?

[@patrickjmt]

+Stay with BlackPink I could! I have a few but should probably make more

[@theuniverseofgaming5980]

Sonic Forces anyone?

[@egehandorum7128]

Your finger is bleeding, master.

[@matthewjames7513]

can someone help me understand why if Ax=0 then det(A) =0?

[@gfcortes1546]

I'm not sure if the question you are asking is correct. A matrix with a determinant equal to 0 must have a NON-ZERO solution x to the equation Ax = 0. If you recall, an invertible matrix A cannot have det(A) = 0. This means that the only solution to Ax = 0 for an invertible matrix is the zero vector. Remember that the very definition of an invertible matrix is one that does not have a non-zero vector x that solves Ax = 0. This, however, is trivial. It follows that if a matrix's determinant is 0, then it must not be invertible, which then implies that there is some non-zero vector x that solves the equation Ax = 0. I hope this answers your question!

[@manuelaidos]

try thinking this way if the vectors in exercises are linear independant then determinant is different from 0 but if they are non linear independant then determinant is equal to 0. Conclusion a basis have always determinant different from 0

[@arunredmi5338]

r u recording new set of vedios?

[@patrickjmt]

+Arun Redmi well, I have a bad tendency to jump all over the place, but if people want more linear algebra, I can head that direction.

[@arunredmi5338]

patrickJMT ..ur vedios are helpfull to me..keep recording..thx

[@hiagooliveira6510]

Awww yes please!!! Thank you so much PatrickJMT. I've been following you for a long time, making sure to subscribe everytime I hop accounts. First, I was seeing your videos about calculating bases for sets and I saw someone commenting asking you to do videos about null spaces and other things, and now you made this video! Awesome man, thanks for listening! Hey btw, if it isn't too much to ask, I have an exercise that I can't find something similar anywhere to clear my doubt. The exercise gives us a "group" (not sure what it is called in english...).. t's as follows: G = { (x, y, z, w): x+y+z = 0, 2x+z+w = 0} and it asks us to check if it's a subspace of R4 and to calculate it's dimension. How to I do that? In the examples I've seen we always have some kind of generic vector but how can I get one from the two equations we have? Cheers, hope this isn't too much to ask!

[@MictorEcta]

I hate linear algebra.

[@patrickjmt]

linear algebra mailed me, and it loves you.

[@danielknapp7389]

patrickJMT I might be biased. I did fail the first exam.

[@MictorEcta]

Why is it so difficult to understand then? I would rather do DE all day

[@md.alief35]

MictorEcta same 😢

[@engnano9688]

i had my midterm today :(

[@patrickjmt]

+Rayan Shammaa you should be happy! It is over! :)

[@engnano9688]

+patrickJMT tomorrow i have differential equation midterm abt convultion theorrm and Fourier series and eigenvectors

[@engnano9688]

+Rayan Shammaa theorem*

[@patrickjmt]

in that case: lucky you!

[@izzatiozir1108]

sign in to my youtube acc just to give likes for your videos. Thank you, your videos help me a lottt!!!! God bless you xx

[@208ream]

Can you private tutor in MATLAB?

[@patrickjmt]

no, i dont know much about it

[@ermiles6472]

The title of this video doesn't make sense mathematically. Please change it to Null Space of a matrix or Null Space of a Linear Transformation.

[@bernarddoherty4014]

Going way too fast