Linear Independence and Linear Dependence, Ex 1

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Linear Independence and Linear Dependence, Ex 1. In this video, I explore the idea of what it means for a set of vectors to be linearly independent or dependent. I then work an example showing that a set of vectors is linearly dependent.

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6 сен 2011

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Комментарии : 329

@shamithpoojary-bk6sj 6 месяцев назад

Anyone watching this video in 2024!!?

@tebabe8827 3 месяца назад

Here 😂

@adeboyeadebayo9115 3 месяца назад

Here..😂

@KeletsoMailula 3 месяца назад

Here😅

@georgekaranja8446 3 месяца назад

Me doing math in campus

@ANyMovies-sc9gz 2 месяца назад

Here, my exam will start in 1 hour 😂

@holdenjones8110 5 лет назад

How to ace all first year math courses: 1- Go to class, try to learn the basics 2- Watch a Khan academy video to "gain some intuition" for subject 3- Watch every relevant Patrick JMT video to practice solving problems 4- Repeat throughout semester

@bharathsf 2 года назад

Brilliant. I did this a few years ago, I still can solve matrices. Just came back to refresh

@yakuzzi35 2 года назад

Oh my God, thanks! This is helpful lol, we can add 3blue1brown to the list of sources to gain intuition

@Itsjustj82 Год назад

Hi, hope you see this question after so many years...I just started my first semester and during the classes I don't seem to understand literally anything that the Prof teaches, I need to go home an study through RU-vid videos to at least to get a sense of what I'm doing.....is it normal to be like this as a first year student?

@Altair4611 Год назад

@@yakuzzi35 only if you see this as a hobby, for most people watching this isnt, they just want to get it over with

@GIWILD Год назад

Even if a donkey does all that he will get all A, you think people work overtime? lol man

@ryanmcguire5532 8 лет назад

You have been my prof for at least 3 classes in uni

@RingxWorld 8 лет назад

this nigga has taught me calculus, lin algebra, stats, i owe this guy my degree

@pbps2005 8 лет назад

Patrick is white!

@ShadowD2C 7 лет назад

he's a honorary niggga

@JattAnmoli 6 лет назад

M'ShadowCC He is my nigga

@chandrapandey822 6 лет назад

Shawn sorry I did get it Is it linear algebra as in lin algebra or lie algebra (lin as in typo)

@islespatrick 9 лет назад

My real math instructor

@MashrufKabir 9 лет назад

islespatrick Amen.

@milkwasabadcholce 8 лет назад

Preach it

@daniloorbolato 7 лет назад

I think that is so because "youtube teachers" are eager to share and teach what they know for no guaranteed return i.e salary. But a lot of "professional teacher" out there are more concerned with their titles and paychecks! Did my first your of Civil heavily backed up by guys like Patrick! If I don't get it there I will surely get it here!

@Rainsong777 6 лет назад

Agreeing on that. Many distance study institutions could make videos like PatrickJMT & make our lives much easier... But, I would come back to Patrick a thousand times over, because he "uncomplicates" Maths & makes it FÜN to learn...... Even makes one look forward to the "next lesson" 😉

@fkncompton7124 4 года назад

@@daniloorbolato do you remember which were some of the most helpful channels for civil

@williamidakwo2953 9 лет назад

To save time if you're asked to determine whether or not the vectors are linearly dependent, Take the determinant, if its = 0 it is linearly dependent if not it is linearly independent.

@Eurosport.Automotive 9 лет назад

that works for square matrices only ;)

@burlapse4113 9 лет назад

As Idakwo William said, you can use the basket weave method for the 3x3 matrix. If the determinant = 0 > its not linearly independent. If det doesn't = 0 > its linearly dependent

@nickweimer6126 9 лет назад

bur lapse other way around...if determinant is equal to zero, its linearly Dependent

@burlapse4113 9 лет назад

nj weimer fixed it xD thanks

@reemaborashed4706 4 года назад

Thank u for saving my 2 remaining braincells's life

@adamfattal9602 3 года назад

First time I watched your videos was in the 8th grade, when I was teaching myself calculus over the summer. I still find myself watching you in college when I need to review over a topic or get some practice. Thank you for all that you do, Patrick! You're changing peoples' lives, so cheers to that

@patrickjmt 13 лет назад

@afiqjenoba well, i hope a student of linear algebra would grasp that : ) and i emphasis that any value of k gives a solution, so it should be pretty clear i think to anyone listening!

@sandblaster007 4 года назад

Such a good tutorial, even 9 years later. Thanks!

@patrickjmt 13 лет назад

@afiqjenoba i am not sure i understand. since the equation has solutions for nonzero values of at least one of: a_1, a_2, a_3 (i show this generically by using the ' k ' notation ) we can say it is linearly dependent.

@youzhenzhang8415 4 года назад

patrick jmt!!! you've helped me all throughout high school and college!! you rock my dude

@Crosswalknorway 9 лет назад

I absolutely love your videos, they are incredibly informative and helpful! Thanks a ton Patrick!

@dapoog721 5 месяцев назад

I love it when my professor just decides to never show up, and still took the test as if he had been there, I literally only have a table of contents and RU-vid

@29ibrahimsayed95 Год назад

Thank you Mr Patrick i remember about 10 years before when i was in 6th or 7th grade i have studied alot of exponential powers from your videos and now studying the concept of linear independence to pass my data science certificate i wholeheartedly respect you ... i am glad you still make videos for the students hope you are in good health :)

@Dirkadirky 10 лет назад

Thanks for making these videos! I'm taking matrix algebra right now but I got a little behind. Your videos have helped me catch up! They're well made and you explain things well

@Turgutgncfb 10 лет назад

Thank you for the video, but I think it is a long way, if you would like to find the case either is it linearly dependence or independence, you can find determinants. If determinants doesn't equal to zero , it means INDEPENDENCE, but if equal then DEPENDENCE (linearly.) BEST REGARDS FROM AZERBAIJAN

@mathe_ma 3 года назад

You can find determinant for square matrices only. Here, it depends on problem whether we will be getting a square matrices or not.

@higgsbp139 10 лет назад

Simple explanations for simple concepts. My teachers somehow managed to make this convoluted. In 15 minutes you explained more than they did in 2+ hours. Kudos and much thanks:)

@Usagimusical 12 лет назад

This is the third year that I have been referencing these math videos, and I must say you're a fantastic instructor! I definitely credit you for developing my passion for math! cheers, Janice :)

@8749236 8 лет назад

The real math teacher! Patrick!

@LifeWithGod99 10 лет назад

appreciate your work, it`s very useful!

@burtonkorten9322 9 лет назад

epic door creek

@CasperLiHongKong 9 лет назад

You are the best math teacher.

@tamzidchowdhury472 3 года назад

I've commented this about 1000 times in your videos, but God Bless You!!

@TheGheezoinky 6 лет назад

Thank you for this and everything else that you do. You just allowed me to ace my midterm. :) GodBless! (if that's the kind of thing you believe in) May the universe be kind to you.

@electrichorror6642 8 лет назад

Man... You deserve more credit you are the man!!!

@fredrikpettersen1 10 лет назад

Yes they do, but there is a difference between knowing the subject and being able to teach it. Patrick is a very skilled teacher, and has helped me a lot. :)

@maybexable 11 лет назад

Thanks so much for your tutorials! You break it down well, easy to understand the concepts.

@firasyam6282 7 лет назад

you have no idea how much this helps. thanks!!!!

@stephendavis1837 3 года назад

You're the best!!! I have passed soooo many classes solely because of your videos.

@patrickjmt 3 года назад

glad i could help you out :)

@mrblini 6 лет назад

god dayum very well explained! my professor has very low energy and its monotoned so I always come back to ya when need help! thx

@dejarno9739 4 года назад

Appreciate you G, you make the most useful videos for the subject.

@fishykey 6 лет назад

You're saving my life !! Thank you so much!!!! Your videos are awesome!

@adrianbogdy 10 лет назад

Great work bro, I really appreciate your work, this lesson was very useful.

@milkwasabadcholce 8 лет назад

Yes!!!! I knew I could depend on pat! Another great video!

@khalidquadmill3339 3 года назад

Ur lectures is helping me in my take home IA right now.

@gdragon1268 7 лет назад

you have saved my life soooooo many times

@DavidMOUSSONGA Год назад

Juste what i was looking for, thank you very much.

@facebooktv6244 6 лет назад

Thank you very much King, you helped me to solve my problem you are very good in explaining

@patrickjmt 12 лет назад

@Usagimusical glad i could help : )

@montywu6205 8 лет назад

Thank you so much Patrick! Your videos saved my ass for so many times!

@BaljitSinghmonty 8 лет назад

+Monty Wu Really????

@MrAlbashiri 11 лет назад

Thank you very very much, your videos helped me a lot in my studies.

@elnulan1 12 лет назад

Thanks, not only did you help me understand linear dependence you helped me to understand that I didn't understand how to properly reduce a matrix. I really thought I knew that! Guess that explains my last test grade

@karlbacalando427 5 лет назад

Thank you for helping me to pass our periodical test

@prabinlamsal5125 5 лет назад

His voice is amazing.

@shannokhan6300 9 лет назад

Ur video lecture has really helped me alot for my exams.Thanks alot............

@jetswhiteout961 9 лет назад

I have a linear algebra and vector geometry final in 2 days this is great review

@mrblini 6 лет назад

my man, again, lots of good stuff, lots of energies in your teaching. very good stuff

@dishamanjunatha7735 7 лет назад

Thank you, you're a blessing!!!!

@MrEvilPandah 12 лет назад

And again PatrickJMT saves the day :> thanks a lot sir!

@muhammadzaid308 3 года назад

I started watching his vids in freshman year high school, now I am a freshman in college

@patrickjmt 13 лет назад

@afiqjenoba no, no i do not think you were undermining my explanation at all : )

@ceciliablomberg1757 10 лет назад

Turgut, i think you are totally right, in this case you can use the determinant and get the answer. But what about if it wasn't a 3*3 Matrix, then you have to go Patricks way, and i actually think it's better to learn Patricks way from the beginning :)) But you are 100 % right you can use the determinant in this case. :)

@williamidakwo2953 9 лет назад

Thanks for the video. I must say it was helpful.

@stefanmilunovic9434 5 лет назад

You are true hero, thank you!

@rufuschen7977 9 лет назад

Thanks!! this is so helpful!

@intensiverleben8998 5 лет назад

I am from germany and can' t speak so good english but your ideas are very good! I understand it! :)

@ninadgandhi3733 4 года назад

Just what i was looking for! Thanks

@RhemaBassey 9 лет назад

Dude thanks man, Now I dont have to sit in class staring at the board confused, like if my teacher is doing magic

@shabirhs4429 3 года назад

Dude you are amazing gonna love this video

@kyrajohnsonx 7 лет назад

this guy is the greatest of all time

@Benjofresh 11 лет назад

You sir are a gentleman and a scholar.

@rajeshkumarponia3772 2 года назад

I m truly impressed with ur English ....n you explain so well

@niklasammitzbllrasmussen2781 10 лет назад

Watched the first one and a half minute, and got exactly the answer I was looking for. :D

@ZakiBadr 4 года назад

Thanks, Mr.Patrick

@amandaniess7028 6 лет назад

I will support u when I finnish my education in 5 years and become rich. But right now I need to support myself. xD Love your videos! Keep up the good work! :)

@keeler1160 6 лет назад

Man I'm so relieved.

@49ramandeepverma77 6 лет назад

Excellent I am 101 percent satisfied easy method by you thank you sir you will our maths professor in gju university

@aniketsalve8558 8 лет назад

thanks bro its help me much

@hin185 11 лет назад

thank you so much!!, it really helps. I am just wondering if you can do a video on LU factorization too?

@chemist7908 5 лет назад

Thank you Patrick !!!

@sijianzhou1856 5 лет назад

ty so much I learned a lot from here.

@edwardzheng8162 6 лет назад

Dude, THANK YOU!

@bowmanzz1 5 лет назад

God Bless you, sir.

@constantinospsaras164 6 месяцев назад

Great video, just a question though. When you found the all-zero row couldn't you stop and say that vectors are linearly dependent? (all-zero row -> infinite solutions)

@orsbertsawe7768 2 года назад

Things become easy for your help 🙏🙏

@ccwing33 8 лет назад

very helpful and clear！thank you

@Hereson 11 лет назад

Thank you!

@ddeakpeti 11 лет назад

finally someone with a great voice!

@adamfattal9602 3 года назад

Racist

@fireflies15 5 лет назад

thank youuu excellent explanation

@Adkorane 11 лет назад

thank u soo much my friend! u realy saved me

@itsjamal96 6 лет назад

Good explanation. Thanks

@JackWutang 6 лет назад

You're a lot better than my college professor.

@AmeliaFox 3 года назад

thank you my dude. legend.

@joncolumbino744 3 года назад

So helpful thanks dude

@anilpirwanii 3 года назад

Why are youtube teachers ALWAYS better than our university professors?

@Rokii19As 2 месяца назад

because they are getting high salary from RU-vid 😂😂

@izzystreaks1807 7 лет назад

By the way Patrick is the reason why I have been getting through engineering school, If you guys really do love him that much I suggest donating to him! He has a website and tbh he deserves it!

@patrickjmt 7 лет назад

$1/mo on Patreon and I would sincerely appreciate it. But why buy the cow when you can get the milk for free? :)

@izzystreaks1807 7 лет назад

LOL xD If you say so!

@vivekpenumaka3871 7 лет назад

clean and clear ....thanks

@ildemax 10 лет назад

i love your videos and u have helped so much thanks!, but i cant seem to figure out to do if you have variables in some of the spots of the matrices how do you find what makes it a linearly dependent or what makes it a linealy independent? i got a test monday im freaking out plzz helpppp

@SPARTAN26MiLLiX 5 лет назад

How'd the test go?

@doommood9911 5 лет назад

@@SPARTAN26MiLLiX brooo i dont know whether this was supposed to be funny but its really cracking me up this night.🤣🤣🤣

@transfo47 4 года назад

@@doommood9911 Only a five year gap after the test. I'm sure he still remembers.

@g_r_s1218 3 года назад

@@transfo47 6 years now.....

@CouponsFTW 11 лет назад

thank the math gods for this video. was learning this in lecture today and i had no idea what was going on D:

@oldisgold4286 5 лет назад

thanks sir, i have learned almost 100% linear independence and dependence..............

@Martina95673 9 лет назад

you're my saviour!

@BaljitSinghmonty 8 лет назад

thanks patrickJMT .

@sansamman4619 6 лет назад

thanks. you are a man. I love you. so much.

@KeeganWoodward 11 лет назад

i heart you. so much. finals would suck if you didn't do what you do.

@mevlanisufi2100 8 лет назад

Why u just dont compute the determinant of the matrix. If the answer is 0, that means they are linearly dependent.

@DDWildlifeConservation 8 лет назад

+Mevlan Isufi At 5:00 why he is getting zero on the 1st row 2nd column? Does anyone know that?

@Marwa-jg9pn 8 лет назад

+Dora Dağlaraşar He is trying to reduce it, to become the identity of a 2 x 2 matrix

@DDWildlifeConservation 8 лет назад

+Marwa AlRuzaiqi thanks man, actually my exam was passed but still thanks.

@Marwa-jg9pn 8 лет назад

No problem, hope you did good :)

@nightmares_ 7 лет назад

You can only find the determinant of a square matrix, and not every matrix you come across will be nxn.

@katiedoucet4748 10 лет назад

ugh answered my question in 47 seconds.... THANK YOU

@spag5296 4 года назад

I'm chuckling right now at how simple this really is when he presents it 🤧

@polychenko 10 лет назад

could you explain it without using the word vector and with no equations? Conceptually can't this be explained simply in a few sentences so non-mathmaticians can understand it?

@k13dude 7 лет назад

what would be the coefficient of dependence of the column vectors of that matrix. I am having a lot of trouble finding how to do this.

@abbykimz 11 лет назад

From the row echolon form and the reduced echolon form, can you tell whether the system is linearly dependent or independent. Also is a unique solution one answer like say I was solving a quadratic equation and got 2 values for x, would that be unique?