Linear combinations and span | Vectors and spaces | Linear Algebra | Khan Academy

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  • Опубликовано: 29 окт 2024

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  • @jennahaines9477
    @jennahaines9477 4 года назад +275

    I have been watching Khan since I was in middle school for math help. Now, I'm at Georgia Tech and STILL getting A's and B's in math because of this man. All my gratitude. You deserve highest honors for teaching the world.

    • @dabidmydarling5398
      @dabidmydarling5398 2 года назад

      What was your high school GPA? I'm a junior and I'm planning to apply for Georgia tech.

    • @jennahaines9477
      @jennahaines9477 2 года назад

      @@dabidmydarling5398 Oh gosh I can't remember. I know I was just shy of getting Zell Miller. So... I think 3.69? Had high ACT scores though and dual enrolled. I think the extra stuff helped since my GPA was just okay in terms of Tech's standards. You can always transfer in- if you really want to go there, you can definitely find a way to do that! it's a great school and I highly recommend it!

    • @dabidmydarling5398
      @dabidmydarling5398 2 года назад +1

      @@jennahaines9477 Hi! I'm also dual enrolled. We have a similar GPA and I am also planning to take the ACT (hopefully I do good on it 🤞🤞)
      Thank you so much for giving your experience. This really gives me perspective on how hard close/far I am.
      Did you do any tech-related extracurriculars? Which extracurriculars should I be doing?

    • @muhammadashshiddieqi8653
      @muhammadashshiddieqi8653 2 года назад +1

      ĹBBBŞČ MÅÝ F W Ù ÑĒĒĐ ĒŞP ČÒÙŘŞĒŞ Ñ ĶÀHVÈÌÑ ČÒFƏĔŞHÒP Ñ MZ.ŞHÌDĐÌĒQÌ ÇHÈÇĶÌŤĹBBBŞČ MÅÝ F W Ù ÑĒĒĐ ĒŞP ČÒÙŘŞĒŞ Ñ ĶÀHVÈÌÑ ČÒFƏĔŞHÒP Ñ MZ.ŞHÌDĐÌĒQÌ ÇHÈÇĶÌŤ

    • @sanguinelinguine
      @sanguinelinguine 2 года назад

      Georgia Tech can be really iffy. It’s probably more based on extracurricular activities. I had 4.0, 33 ACT and got in, while my friend had 4.0, 35 ACT and didn’t. I’d say if you have solid academics, really work on leadership and community service roles.

  • @kyledomen2627
    @kyledomen2627 4 года назад +112

    This quote really helped me understand the concept.
    "If vector a and vector b spans R2, that tells us any vector in R2 can be represented by a linear combination of vector a and vector b"

  • @adrianchivas2014
    @adrianchivas2014 9 лет назад +160

    Thank you khan for helping me understand this. I am taking Linear Algebra my sophomore year in college. Anyways, all I have to say is that you are the real MVP!!!
    Always, remember that you are changing lives and I am in college because of you my friend. On track to become an Electrical Engineer.
    On behalf of everyone that admires you, Thank you!!!

    • @benpotter3278
      @benpotter3278 7 лет назад

      adrianchivas2014 I am In 7th grade and I'm learning this

    • @jacobm7026
      @jacobm7026 6 лет назад +18

      by the way, i'm in kindergarten and am loving vector spaces and the alphabet

    • @Dan-gc3ke
      @Dan-gc3ke 6 лет назад +7

      smh I'm in pre-school and I'm learning this

    • @ProLeopardx1
      @ProLeopardx1 5 лет назад +2

      @@katb9776 Nah, I don't know what school you went to but I wasn't taught vectors until calculus. I'm learning linear algebra right now after Calc 1, 2, and 3 (multivar). It's combined with multivar calc at my college and I hate it. Everyone's doing far worse in this than they did in calc 3.

    • @SanaZub
      @SanaZub 5 лет назад +4

      im in daycare and im learning this!!! just turned 3 yesterday! woot woot MATRICES R LITTTTTTTT

  • @jappmayo1220
    @jappmayo1220 9 лет назад +221

    I just paused this halfway to say THANK YOU for helping me to understand this!

    • @Station1643
      @Station1643 5 лет назад

      but u asian, why u no understande ?

    • @uddipanbaruah6021
      @uddipanbaruah6021 4 года назад

      @@Station1643 abbeeyyy kije hbo mane

    • @Station1643
      @Station1643 4 года назад

      @@uddipanbaruah6021 abbe me no understand Indian

    • @uddipanbaruah6021
      @uddipanbaruah6021 4 года назад

      @@Station1643 its ok.. Jai Ai Axom

    • @mahadevhatti5228
      @mahadevhatti5228 4 года назад

      @@Station1643 doe youe understande whate youe saide ??

  • @nlnrose
    @nlnrose 8 лет назад +42

    ... you explain this better than my college matrix algebra teacher... wow I actually am starting to understand this.

  • @mrjoni54
    @mrjoni54 10 лет назад +91

    3:47-3:52 " Hey Sal, why are you even introducing this idea of an linear combination?"
    "Beacause I wanna!"

  • @WalidFeghali
    @WalidFeghali 13 лет назад +74

    I passed Linear Algebra because of these videos. You're the best, Khan!

    • @pinklady7184
      @pinklady7184 3 года назад +1

      Nah no noo, he da best and *BESTEST!*

    • @majed1911
      @majed1911 Месяц назад +2

      13 years later I hope you can answer this question
      What can I do to practice in the best way possible

    • @WalidFeghali
      @WalidFeghali Месяц назад +1

      @@majed1911 The best way to study is to start small. Start with the easiest stuff, and learn it well. If you don't understanding something early on, basic things, talk to a tutor in class, don't go straight to the professor. The tutors are great because they were where you are just recently. 13 years go by fast!

  • @vanessang4216
    @vanessang4216 8 лет назад +33

    You are a true blessing to the world

  • @economicswithozzy
    @economicswithozzy 7 месяцев назад +35

    2024 maths is still same 😂😂😂

    • @Got-it747
      @Got-it747 4 месяца назад +6

      Because reality is still the same

    • @BAMEADManiyar
      @BAMEADManiyar 24 дня назад

      ​@@Got-it747true 🤞

  • @EwoudCP
    @EwoudCP 14 лет назад +7

    Wow. This is really useful. I've been trying to make sense of the idea of the span, but I tend to see things other people don't. More frustratingly, I tend to not see things that other people do. Thanks for the video. I'll definitely keep your playlists in my bookmarks.

  • @TheBlackZoe
    @TheBlackZoe 7 лет назад +6

    Using this "pseudo-proof" system: drawing the vectors as a visual method is such a great representation of the idea of vector space. Thank you. Greetings from Greece.

  • @eleazararce5716
    @eleazararce5716 Год назад +2

    About to take this class for a second times after 13 years of being out of school. Its should be fun and interesting this time around!! I will be utilizing these videos too!!

  • @selingermann5599
    @selingermann5599 5 лет назад +7

    I have finally reached ENLIGHTENMENT!
    Thank you.

  • @alechenderson8410
    @alechenderson8410 Год назад +6

    shoutout to anyone else with a bad linear algebra prof

  • @mabeklvista
    @mabeklvista 12 лет назад +3

    why is this 10 times better explained than in lectures? they go so fast, here i can learn on my own speed. Thank you Sal!

  • @Zurh1994
    @Zurh1994 12 лет назад +5

    They've explained me this for 3 consecutive years. Every year I fear this explanation because I can't picture it, I don't know why is it useful, and now it's really like I can see the truth hahaha.
    How can you explain everything so nicely in every single video and my teachers be so useless? XD

  • @bobbypesch5220
    @bobbypesch5220 4 года назад +4

    vibing in my dorm rn but had to give a shoutout to Sal, this man got me into college

  • @Fallen_Fly
    @Fallen_Fly 12 лет назад +1

    Thank you, linear algebra and differential equations has changed my opinion about math from completely in love to loathing it. Hopefully with your videos I can get my passion back.

  • @VSpooner
    @VSpooner Год назад

    this makes understanding the math so much better, rather than just showing the process you manage to show the process of understanding.

  • @nathandrouillard2927
    @nathandrouillard2927 7 лет назад

    Thank you. These concepts aren't even that hard, but my prof speaks in VERY broken English and teaches very poorly on top of that so I absorb close to nothing in my lectures. These videos are a godsend

  • @roxymang1
    @roxymang1 10 лет назад +6

    so helpful! i was stuck on a question all day reading the textbook, then i watched this video and now it's clear :D

    • @danteeep
      @danteeep 7 лет назад

      exactly what happened to me

  • @danielcohen9637
    @danielcohen9637 4 года назад +2

    How do you know so much? You know math, accounting,business, computers,physics and more.

  • @waseem1173
    @waseem1173 13 лет назад

    Now thats a real teacher. man i love you . you're a life saver

  • @Batooya
    @Batooya Год назад

    idk if you (the person teaching in the vid) will ever read this but I, and I'm sure others as well, have come to find you and your lessons to be really comforting

  • @necatiakpnar5677
    @necatiakpnar5677 7 лет назад

    your video uploaded in 2009 but still helping to people understand algebra. Thanks for everything!

  • @drahoo302
    @drahoo302 8 лет назад +6

    15:46 You Sir, just wrote it perfectly :-)

  • @bgraaman89
    @bgraaman89 2 года назад

    I might receive flak for saying this, but this Linear combination video of yours is much better than Dr. Gilbert Strang's MIT video. You've explained it much better than he did. Thank you.

  • @krose7406
    @krose7406 11 лет назад +12

    i gave up and just started watching the lectures DURING class!!

  • @lilonepj
    @lilonepj 4 года назад

    Thanks for the videos. Please add practice problems for the linear algebra topics!! I can only find 4 practice sets for the vectors section.

  • @slykni8
    @slykni8 2 месяца назад

    Wow, you are a real genius.
    You just cleared my doubt.❤❤❤

  • @fadlmasri
    @fadlmasri 3 года назад +1

    the fact that this vid is 11 years old and it still helped me is outrageous

  • @haro123ish
    @haro123ish 13 лет назад

    love you man, i always wondering what a span was. my teachers have failed to explain this so far. thank you

  • @SochoChun
    @SochoChun 13 лет назад +1

    sweet... it's much better than my professor's lessons, this is a really good revision lesson before my test

  • @SporkyG
    @SporkyG 11 лет назад +7

    he corrects it at 19:26 :)

  • @witnessforchrist7778
    @witnessforchrist7778 6 лет назад +1

    Not even 3 minutes into it, I've learned more from Khan Academy so far than 8 weeks of linear algebra in class. My teacher sucks at explaining, he's all over the place, he has a strong accent, his hand writing sucks, nor does he explain terminology.

  • @rowanfrankenbach3625
    @rowanfrankenbach3625 4 месяца назад +1

    7:57 the "SPAN" he said it with gusto lmao. sal is legendary

  • @McDreamOn
    @McDreamOn 12 лет назад

    Have an exam tomorrow over this stuff and I just had an ah ha! moment!!!!! So much clearer than my professor!

  • @sherajr
    @sherajr 15 лет назад +2

    I'm so glad I found this before my midterm!!

  • @publicanimal
    @publicanimal 13 лет назад

    You are a god. with the graphical representation of vector space R2 I finally understood the concept of linear combos. thanks

  • @desxse6309
    @desxse6309 5 лет назад +1

    Thank you so much. After I watch this, I understand linear independent, linear dependent and why free variable relate to them.

  • @evelynecheung1905
    @evelynecheung1905 4 года назад +2

    2020 and this is still saving lives thank you so much !!

  • @zhongqiren6794
    @zhongqiren6794 9 лет назад +1

    God bless you, Khan, Thank you very very very very much.

  • @imegatrone
    @imegatrone 12 лет назад

    I Really Like The Video Understanding linear combinations and spans of vectors From Your

  • @amayashenuri1147
    @amayashenuri1147 8 месяцев назад

    just an amazing teacher❣

  • @theotydingco7987
    @theotydingco7987 9 лет назад +19

    18:00
    How do you get from 3c2 = x2 - 2x1
    to c2 = 1/3(x2 - x1)
    Where does the "2" in -2x1 go?

    • @mandy1339
      @mandy1339 9 лет назад

      +Theo Tydingco did you watch the video all the way to the end? you can see what happens

    • @theotydingco7987
      @theotydingco7987 9 лет назад +2

      +mandy1339 yeah figured it out.

    • @patmull1
      @patmull1 8 лет назад +1

      +Theo Tydingco Yeah.... I was like "PHEW... thanks god" :D

    • @sahil5185
      @sahil5185 7 лет назад +1

      Yeah I was so stressed out until he corrected it lol!

  • @adam.phelps
    @adam.phelps 14 лет назад

    @Ace12174 He multiplied by -2 so he could find one variable at a time - which in this case wasC2 - so after he found the value of C2 he could find the value of C1. Its called solving a system of linear equations by using elimination.

  • @danielgonzalezisaiev9643
    @danielgonzalezisaiev9643 11 лет назад

    Love your videos! The thing that makes great lecture videos is the person talking and their pedagogic skills and you sir, YOU GOT EM'! Great presentation, great understandable language, thanks so much for your videos!

  • @river.
    @river. 3 года назад

    13:11 finally understood span

  • @wjestick
    @wjestick 11 лет назад

    Magic formula. Watch this video before you cover LA in the lectures. Then use the lectures as revision! It is a lot easier to pay attention when you are actively listening.
    And with two reviews you are much more likely to retain the material.

  • @tsaras2838
    @tsaras2838 3 года назад

    your voice gives me hope.

  • @omardanial7351
    @omardanial7351 5 лет назад +7

    Thanks Sir Salman Khan..
    You saved my semester of engineering.

  • @fliskmayhem
    @fliskmayhem 13 лет назад

    @LostAngel01234 First of all, you'll need at least 3 diffrent vectors (call them v_1, v_2 and v_3). Each with dimension 3, so they'll look like (x,y,z). Second, it must be impossible to write one of these vectors as a linear combination of the other 2 vectors. I.e. : c_1 v_1 + c_2 v_2 + c_3 v_3 = (0,0,0) only if c_1 = c_2 = c_3 = 0, the three vectors span R3. If there's another solution for the c_i's, it means the vectors span up a plane or a straight line in R3, but not whole R3.

  • @towbsmedia
    @towbsmedia 3 года назад

    Cheers brother; great job. thank you

  • @fauziahassan9938
    @fauziahassan9938 3 года назад

    Hey sir thank u sooo much for this video .....

  • @hai2410
    @hai2410 14 лет назад

    @Ben1220 and @thomapple
    I think he's right actually. R^n is n-tuples of real numbers. If you're working in R^2, you have two dimensions to work in and so you get [x1,x2], R^3 [x1,x2,x3], so it follows from that.

  • @kjz8923
    @kjz8923 5 лет назад

    thank you Khan ! i’m taking linear algebra in my junior year in high school! This video helped a lot!

  • @Menor55672
    @Menor55672 3 года назад

    Thank you Mr. Khan

  • @Ben1220
    @Ben1220 14 лет назад

    You're absolutely right, it doesn't matter how many vectors you have, linear combinations are defined for any set of vectors. He probably should have chosen a different name for the first n, but this doesn't matter if you realise that the two n's are different.
    Well done for spotting that :P

  • @ExecutiveGoth
    @ExecutiveGoth 4 года назад

    This saved me for my high school exams thanks so much

  • @chiupaulpaul
    @chiupaulpaul 7 лет назад

    I'm so glad you made this video.

  • @krishonweb
    @krishonweb 5 лет назад

    I love you man! What an explanation

  • @sophmcamp
    @sophmcamp 5 лет назад

    binging many of these videos before my final because I rarely understood my professor’s explanations

  • @dansam5467
    @dansam5467 5 лет назад

    Thanks for the help

  • @bryannamelenhorst
    @bryannamelenhorst 14 лет назад

    thank the lord i found these video's. you are an amazing teacher!

  • @damnfreakingsien
    @damnfreakingsien 5 лет назад

    THANK YOU!!! i was finally able to visualise this frustrating concept.
    Time to rush my homework before deadline...... :(

  • @shibsankar4569
    @shibsankar4569 5 лет назад

    Best and simple to understand

  • @talha6k
    @talha6k 14 лет назад

    You are great! God bless....

  • @carolllj
    @carolllj 4 года назад

    thank u so much my lifesaver

  • @yusuf1597
    @yusuf1597 8 лет назад +26

    At 6:18 Sal turns into a Canadian.

    • @dybiosol
      @dybiosol 8 лет назад

      I see what you did there!

    • @ataadi1460
      @ataadi1460 6 лет назад

      Everyone saw what he did there.Any issues?

  • @fluffio2976
    @fluffio2976 7 лет назад +5

    *Comes back an hour after having paused the video* "The actual fuck has he drawn."

  • @zack_120
    @zack_120 3 года назад

    4:50 - the graphic coordinates in increments of 2, not 1, is counterintuitive, reducing lecture efficiency.

  • @JesusAxolotl
    @JesusAxolotl 13 лет назад

    @Feroyn totally agree!

  • @shrutikasansaria8499
    @shrutikasansaria8499 4 года назад

    The explanation is just awesome 🤩

  • @edgbaston149
    @edgbaston149 3 года назад

    Thank you so much Sir🙏

  • @satyajeetbunty6550
    @satyajeetbunty6550 4 года назад

    Thank you 🙏

  • @MrAntihumanism
    @MrAntihumanism 11 лет назад +1

    love this!!

  • @nonyvip1
    @nonyvip1 11 лет назад

    شكررا جزيلااا

  • @razberrycreme
    @razberrycreme 12 лет назад +1

    You are an amazing teacher. Thank you!

  • @gibbytravis
    @gibbytravis 4 месяца назад +1

    @18:22 how did you go from 3c2 = x2 - 2x1 to c2 = 1/3(x2 - x1)? Is that a mistake? Did you mean to say c2 = 1/3(x2 - 2x1)?

    • @gibbytravis
      @gibbytravis 4 месяца назад

      Never mind. I see that you corrected it.

  • @Earphony
    @Earphony 13 лет назад

    OOOOOOOOOOOOOOOOOOOOOOOOOOO now i get it.
    Thx Sal.

  • @oluwatoba11
    @oluwatoba11 13 лет назад

    I think I need to take some moment of pause sometimes in the exams too! Great guy!!!

  • @jhl849
    @jhl849 7 лет назад

    Thank you for very good explanation.

  • @alikoteich6639
    @alikoteich6639 5 лет назад

    Your crosshair is amazing for csgo

  • @doaard9174
    @doaard9174 6 лет назад

    شكرا

  • @mediocremathtutorials2098
    @mediocremathtutorials2098 9 лет назад

    All the linear combinations of two vectors (in R3) are all of the points on a family of planes, when tied to a single point it represents a single plane. This is because the parametric form of a point P on a plane is P= a +Sb +Tc. Where a is a known point on the plane, S and T are scalars, and b and c are vectors ON the plane.

  • @shashankverma8939
    @shashankverma8939 4 года назад

    thank you sir

  • @Nandeesh_N
    @Nandeesh_N 3 года назад

    @Khan Academy Should the scalar value which is used to multiply the vector belongs to a real value? if yes, at the end, the c2 obtained is a fraction.

  • @khashya786786
    @khashya786786 12 лет назад

    This is real charity work!

  • @azfanification
    @azfanification 15 лет назад

    you rock my khan!!

  • @danteeep
    @danteeep 7 лет назад

    I can't thank you enough for this video

  • @NikhilXLII
    @NikhilXLII 12 лет назад

    Thank you so much. This completely cleared up all the material I'd learned in class.

  • @Ace12174
    @Ace12174 14 лет назад

    This is definitely helping me understand span. It's starting to sink in! lol Thanks! There's one question I have though, why do you multiply (at 17:24) when finding any C1 and C2 by -2? thanks =) (Grade 12 Calculus and Vectors)

  • @raymondkazibweAwesomenessjust
    @raymondkazibweAwesomenessjust 10 лет назад

    glad you noticed that error !I was gobsmacked initially!

  • @truesoundwave
    @truesoundwave 3 года назад

    4:00 Yep.

  • @organicstore8557
    @organicstore8557 6 лет назад

    Great job Sir .

  • @Robertlavigne1
    @Robertlavigne1 12 лет назад

    I cant tell you how much I love this man!! I want to kiss him on the mouth!!! 4 days till my LA final and I was getting so frustrated. Now its all clear!! Thank you so much!!!

  • @disornr
    @disornr 14 лет назад

    God bless you!!

  • @Edwrath
    @Edwrath 13 лет назад +7

    My University Day:
    -Sleep through morning lectures.
    -Watch khanacademy versions of my lectures
    -Play guitar all afternoon

  • @arnabpaul7215
    @arnabpaul7215 7 лет назад

    wonderful lecture

  • @ceciliaosorio7746
    @ceciliaosorio7746 6 лет назад

    Thank you so much for this very helpful video!