❖ Linear Independence and Linear Dependence, Ex 1 ❖

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  • Опубліковано 22 жов 2024

КОМЕНТАРІ • 343

  • @holdenjones8110
    @holdenjones8110 5 років тому +329

    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
      @bharathsf 3 роки тому +5

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

    • @yakuzzi35
      @yakuzzi35 2 роки тому +4

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

    • @Itsjustj82
      @Itsjustj82 2 роки тому +3

      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 UA-cam 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
      @Altair4611 2 роки тому +2

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

    • @GIWILD
      @GIWILD Рік тому +3

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

  • @ryanmcguire5532
    @ryanmcguire5532 8 років тому +604

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

    • @RingxWorld
      @RingxWorld 8 років тому +151

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

    • @pbps2005
      @pbps2005 8 років тому +25

      Patrick is white!

    • @ShadowD2C
      @ShadowD2C 8 років тому +96

      he's a honorary niggga

    • @JattAnmoli
      @JattAnmoli 7 років тому +11

      M'ShadowCC He is my nigga

    • @chandrapandey822
      @chandrapandey822 6 років тому +1

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

  • @williamidakwo2953
    @williamidakwo2953 9 років тому +184

    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
      @Eurosport.Automotive 9 років тому +49

      that works for square matrices only ;)

    • @burlapse4113
      @burlapse4113 9 років тому +2

      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
      @nickweimer6126 9 років тому +12

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

    • @burlapse4113
      @burlapse4113 9 років тому +3

      nj weimer fixed it xD thanks

    • @reemaborashed4706
      @reemaborashed4706 4 роки тому +12

      Thank u for saving my 2 remaining braincells's life

  • @islespatrick
    @islespatrick 9 років тому +350

    My real math instructor

    • @MashrufKabir
      @MashrufKabir 9 років тому +6

      islespatrick Amen.

    • @milkwasabadcholce
      @milkwasabadcholce 8 років тому +2

      Preach it

    • @daniloorbolato
      @daniloorbolato 7 років тому +8

      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
      @Rainsong777 6 років тому +2

      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
      @fkncompton7124 4 роки тому +1

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

  • @adamfattal9602
    @adamfattal9602 3 роки тому +12

    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

  • @Turgutgncfb
    @Turgutgncfb 10 років тому +15

    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
      @mathe_ma 4 роки тому +1

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

  • @shamithpoojary-bk6sj
    @shamithpoojary-bk6sj 9 місяців тому +112

    Anyone watching this video in 2024!!?

  • @sandblaster007
    @sandblaster007 4 роки тому +10

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

  • @dapoog721
    @dapoog721 8 місяців тому +1

    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 UA-cam

  • @DavidMOUSSONGA
    @DavidMOUSSONGA Рік тому +1

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

  • @youzhenzhang8415
    @youzhenzhang8415 4 роки тому +2

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

  • @29ibrahimsayed95
    @29ibrahimsayed95 2 роки тому

    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 :)

  • @tamzidchowdhury472
    @tamzidchowdhury472 4 роки тому +1

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

  • @Dirkadirky
    @Dirkadirky 10 років тому +3

    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

  • @higgsbp139
    @higgsbp139 11 років тому +1

    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:)

  • @khalidquadmill3339
    @khalidquadmill3339 3 роки тому

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

  • @mmxo2002
    @mmxo2002 Місяць тому +2

    here I am, a 22 year old, watching this after 13 years of posting. Crazy to think about!

    • @patrickjmt
      @patrickjmt  Місяць тому +2

      haha, here i am replying to it 13 years after making it :)

  • @marjanalhaque9865
    @marjanalhaque9865 3 роки тому

    you also check by solving determinant.if the determinant is zero(0) then it will be dependent otherwise independent

  • @Usagimusical
    @Usagimusical 13 років тому +2

    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 :)

  • @fredrikpettersen1
    @fredrikpettersen1 11 років тому +2

    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. :)

  • @stephendavis1837
    @stephendavis1837 4 роки тому

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

    • @patrickjmt
      @patrickjmt  4 роки тому

      glad i could help you out :)

  • @izzystreaks1807
    @izzystreaks1807 7 років тому

    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
      @patrickjmt  7 років тому +1

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

    • @izzystreaks1807
      @izzystreaks1807 7 років тому

      LOL xD If you say so!

  • @serendipitous5497
    @serendipitous5497 5 років тому +1

    Well explained

  • @8749236
    @8749236 9 років тому +3

    The real math teacher! Patrick!

  • @MrAlbashiri
    @MrAlbashiri 11 років тому +1

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

  • @jetswhiteout961
    @jetswhiteout961 9 років тому +1

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

  • @orsbertsawe7768
    @orsbertsawe7768 2 роки тому

    Things become easy for your help 🙏🙏

  • @Benjofresh
    @Benjofresh 12 років тому

    You sir are a gentleman and a scholar.

  • @elnulan1
    @elnulan1 13 років тому

    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

  • @Turgutgncfb
    @Turgutgncfb 10 років тому

    3*3 Matrix , in this case, you shoul finde rank of matrix, if rank of matrix smaller than number of variables, it means linearly dependent, but if rank of matrix equal or greater than number of variables , then linearly independant

  • @ceciliablomberg1757
    @ceciliablomberg1757 10 років тому +1

    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. :)

  • @mrblini
    @mrblini 6 років тому

    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

  • @karlbacalando427
    @karlbacalando427 6 років тому

    Thank you for helping me to pass our periodical test

  • @TheGheezoinky
    @TheGheezoinky 7 років тому +2

    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.

  • @firasyam6282
    @firasyam6282 7 років тому

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

  • @ZakiBadr
    @ZakiBadr 4 роки тому

    Thanks, Mr.Patrick

  • @burtonkorten9322
    @burtonkorten9322 9 років тому +50

    epic door creek

  • @intensiverleben8998
    @intensiverleben8998 5 років тому

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

  • @Crosswalknorway
    @Crosswalknorway 10 років тому +4

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

  • @drewbrouwer6701
    @drewbrouwer6701 12 років тому

    He associates a1, a2, and a3 with a new variable, k, to show that there are infinitely many non-trivial solutions to the set of equations described by the matrix. Not only does this prove that the set of vectors is linearly dependent, but a set of solutions is described by [a1=(-1/2)k, a2=(-5/8)k, and a3=k] for which k can be any real number. If you plug any real number in for k, find the associated a1, a2, a3, and plug these into your definition of linear (in)dependence the result will be zero.

  • @davidfield5295
    @davidfield5295 8 років тому +41

    Excellent videos, I always wonder who the losers are who give these videos thumbs down

    • @choodooloo8133
      @choodooloo8133 8 років тому +46

      Disgruntled professors

    • @Warningcode1
      @Warningcode1 8 років тому +5

      David Field kids who are dumb and still don't get it

    • @raghuvamsiu1287
      @raghuvamsiu1287 7 років тому

      You have answered it David. "Losers!!".

    • @adv3nturetime
      @adv3nturetime 6 років тому

      Not everybody learns the same way.

  • @montywu6205
    @montywu6205 9 років тому +3

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

  • @patrickjmt
    @patrickjmt  13 років тому +6

    @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!

  • @shannokhan6300
    @shannokhan6300 9 років тому +1

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

  • @rajeshkumarponia3772
    @rajeshkumarponia3772 3 роки тому

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

  • @constantinospsaras164
    @constantinospsaras164 9 місяців тому

    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)

  • @facebooktv6244
    @facebooktv6244 6 років тому

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

  • @maraltsogt3511
    @maraltsogt3511 8 місяців тому +7

    guess who is watching this after 12 years later. ME

  • @izzystreaks1807
    @izzystreaks1807 7 років тому

    Why do we want to 0 out the number in row 1 column 2? it was the last matrix operation you did before determining the non-trivial solutions.

  • @muhammadzaid308
    @muhammadzaid308 4 роки тому +2

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

  • @49ramandeepverma77
    @49ramandeepverma77 6 років тому

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

  • @maybexable
    @maybexable 11 років тому +1

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

  • @dejarno9739
    @dejarno9739 4 роки тому

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

  • @CasperLiHongKong
    @CasperLiHongKong 10 років тому +2

    You are the best math teacher.

  • @mevlanisufi2100
    @mevlanisufi2100 9 років тому +16

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

    • @DDWildlifeConservation
      @DDWildlifeConservation 9 років тому +2

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

    • @Marwa-jg9pn
      @Marwa-jg9pn 9 років тому +1

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

    • @DDWildlifeConservation
      @DDWildlifeConservation 9 років тому +2

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

    • @Marwa-jg9pn
      @Marwa-jg9pn 9 років тому +1

      No problem, hope you did good :)

    • @nightmares_
      @nightmares_ 8 років тому +6

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

  • @kyrajohnsonx
    @kyrajohnsonx 7 років тому

    this guy is the greatest of all time

  • @keeler1160
    @keeler1160 6 років тому

    Man I'm so relieved.

  • @electrichorror6642
    @electrichorror6642 8 років тому

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

  • @thefirstsurvivor
    @thefirstsurvivor 7 років тому +3

    if you see a free variable doesn tthat automatically mean linearly dependent

  • @patrickjmt
    @patrickjmt  13 років тому

    @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.

  • @ninadgandhi3733
    @ninadgandhi3733 4 роки тому

    Just what i was looking for! Thanks

  • @agapitoserrato9126
    @agapitoserrato9126 4 роки тому

    I got this video in my recommended today. But I used your great videos to get through lots of math and chemistry classes. I missed you PatrickJMT and I'm glad I found you again

  • @LifeWithGod99
    @LifeWithGod99 11 років тому +8

    appreciate your work, it`s very useful!

  • @fishykey
    @fishykey 6 років тому

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

  • @vasanthkumarcroos8605
    @vasanthkumarcroos8605 3 роки тому

    Excellent sir

  • @KeeganWoodward
    @KeeganWoodward 12 років тому

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

  • @HoLeeeeFuck
    @HoLeeeeFuck 2 місяці тому

    @patrickjmt at 5:01 why should you have a zero in the first row, second column?

  • @oldisgold4286
    @oldisgold4286 5 років тому

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

  • @williamidakwo2953
    @williamidakwo2953 9 років тому

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

  • @NiranjanRavikumar7
    @NiranjanRavikumar7 11 років тому

    Hey in my mathematics book it written like "if the Eigen values are non-repeated then then it has linearly independent Eigen vectors". But my say on this is : " If they are non-repeated then how is it linearly independent because all the Eigen values must be zero in a linearly independent combination. Thanks in advance :)

  • @mohammadahmermalick7869
    @mohammadahmermalick7869 6 років тому

    everything goes easy when you teach

  • @itsjamal96
    @itsjamal96 6 років тому

    Good explanation.
    Thanks

  • @bowmanzz1
    @bowmanzz1 6 років тому

    God Bless you, sir.

  • @prabinlamsal5125
    @prabinlamsal5125 5 років тому +1

    His voice is amazing.

  • @chemist7908
    @chemist7908 5 років тому

    Thank you Patrick !!!

  • @polychenko
    @polychenko 11 років тому +2

    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?

  • @JackWutang
    @JackWutang 6 років тому

    You're a lot better than my college professor.

  • @BaljitSinghmonty
    @BaljitSinghmonty 9 років тому

    thanks patrickJMT .

  • @stefanmilunovic9434
    @stefanmilunovic9434 5 років тому

    You are true hero, thank you!

  • @yashwanth7978
    @yashwanth7978 2 роки тому

    So, can we say that independent matrices have unique solution?

  • @adrianbogdy
    @adrianbogdy 11 років тому +2

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

  • @NotTheRealBassKitten
    @NotTheRealBassKitten 7 років тому

    so since there's a row of entirely zeros, you could say that the vectors have an infinite amount of solutions?

  • @praveenpatil4717
    @praveenpatil4717 4 роки тому

    Sir would be please solve: Find A(W), Where W is spanned by (1,2,3) and (0,4,-1)

  • @shabirhs4429
    @shabirhs4429 3 роки тому

    Dude you are amazing gonna love this video

  • @patrickjmt
    @patrickjmt  13 років тому

    @Usagimusical glad i could help : )

  • @sanashahid324
    @sanashahid324 4 роки тому

    From which book you took this question ? Kindly reply it will mean a lot

  • @wagyu2733
    @wagyu2733 3 роки тому

    probably should of watch this video before my specialist maths exam

  • @vivekpenumaka3871
    @vivekpenumaka3871 7 років тому

    clean and clear ....thanks

  • @mianmajid87
    @mianmajid87 10 років тому

    since this is a square matrix we can find the determinant of the matrix.
    it comes out to be 0.. which also confirms that it is Linearly dependent..

  • @HoangDucNuyen
    @HoangDucNuyen 9 років тому

    A = [2 4 6;7 5 3;1 4 6];
    B = [2 4 6; 7 5 3;4 8 12];
    Find the linear dependent and linear independent rows in the matrix A and B????

  • @mrblini
    @mrblini 6 років тому +3

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

  • @PaxiKaksi
    @PaxiKaksi 6 років тому

    shouldn't the conversion from vector to matrix be done differently ?
    I mean column 1 should have been
    1 , 4 , 3
    and not
    1, -2, 0 ?

  • @AmeliaFox
    @AmeliaFox 3 роки тому

    thank you my dude. legend.

  • @redhotkido
    @redhotkido 11 років тому

    have a test soon yay for this vid.

  • @milkwasabadcholce
    @milkwasabadcholce 8 років тому

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

  • @joncolumbino744
    @joncolumbino744 4 роки тому

    So helpful thanks dude

  • @vibhanshushukla3430
    @vibhanshushukla3430 Рік тому

    When we say vectors are LI then it means every scalar associated with vectors are zero and we also know that these scalar belongs from field F and field must be abelian group with respect to multiplication so it is obvious that it will follow property of *existence of inverse*. But 0 has no multiplicative inverse.
    Then how these scalars (which are zero) can be elements of a field ?
    😢

  • @sijianzhou1856
    @sijianzhou1856 5 років тому

    ty so much I learned a lot from here.

  • @ildemax
    @ildemax 11 років тому +4

    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
      @SPARTAN26MiLLiX 6 років тому +1

      How'd the test go?

    • @doommood9911
      @doommood9911 5 років тому

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

    • @transfo47
      @transfo47 5 років тому +1

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

    • @g_r_s1218
      @g_r_s1218 4 роки тому +1

      @@transfo47 6 years now.....

  • @hin185
    @hin185 12 років тому

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