Matrices to solve a system of equations | Matrices | Precalculus | Khan Academy

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  • เผยแพร่เมื่อ 30 ม.ค. 2025

ความคิดเห็น • 454

  • @pranavsood2058
    @pranavsood2058 9 ปีที่แล้ว +874

    "I hope i'm not boring you".
    Me: No Sal, you are amazing you are helping me with my exam

  • @natassciabryce2946
    @natassciabryce2946 8 ปีที่แล้ว +346

    Thank God i found you cuz my math teacher messed me the hell up

    • @LizbethAyala
      @LizbethAyala 7 ปีที่แล้ว

      NATASSCIA BRYCE 😂

    • @monstercl1668
      @monstercl1668 7 ปีที่แล้ว

      NATASSCIA BRYCE

    • @duck8024
      @duck8024 6 ปีที่แล้ว

      Same here

    • @random_scum
      @random_scum 6 ปีที่แล้ว +2

      I feel you, bro.

    • @theodrinksman4119
      @theodrinksman4119 5 ปีที่แล้ว +3

      Tbh i learn more by watching this 16mins. Video than my teacher explaining it for 2 hours

  • @metalheadlass
    @metalheadlass 11 ปีที่แล้ว +159

    When I watch these videos, I really start to wonder why my teacher gets paid. This guy is doing a service to humanity by doing this, honestly. Wouldn't be here if my teacher was worth anything, so thanks for the real education.

  • @loneranger7831
    @loneranger7831 ปีที่แล้ว +55

    This video is 15 years old, and it is still super helpful.

    • @Twaj_
      @Twaj_ 6 หลายเดือนก่อน

      pythagoras was born 2594 years ago and his theorem is still helpful, math is cool like that

  • @MWSART
    @MWSART 9 ปีที่แล้ว +140

    beyond everything you got a great voice sir..soothes the ear

  • @joeytrevino2903
    @joeytrevino2903 5 ปีที่แล้ว +61

    I have an exam in 2 days and my professor basically relies on us learning from the book and not him teaching us. I have to get to video number 47 in this wonderful playlist. I am currently on video 7 and I have already learned things that I didn't know I needed to learn. Thank you for this collection.

    • @travisc8406
      @travisc8406 ปีที่แล้ว +1

      lmao a bit late but how did it go?

    • @jozie892
      @jozie892 ปีที่แล้ว +3

      @@travisc8406 if I remember correctly this was my precal class and I passed. Also graduated but thanks. Video was helpful.

  • @TheReck12
    @TheReck12 7 ปีที่แล้ว +477

    My teacher skipped matrices in algebra 2 so here I am in pre calc and I have no idea what any of this is

    • @brucexu313
      @brucexu313 5 ปีที่แล้ว +16

      nah it's ok I'm in IB HL and have no idea what any of this is

    • @xx-sg8wx
      @xx-sg8wx 5 ปีที่แล้ว +13

      I never learned matrices until the end of AP Calculus BC lol

    • @ghostofmisao.
      @ghostofmisao. 5 ปีที่แล้ว +18

      I'm in Algebra 2 rn and I don't understand this stuff 😂

    • @omariqbalhamid280
      @omariqbalhamid280 4 ปีที่แล้ว +1

      Matrix starts in precalc

    • @harleighstringer
      @harleighstringer 4 ปีที่แล้ว +13

      ive taken literally precal, cal 1,2, and 3 and don't remember ever doing these. now im in linear algebra struggling and beyond confused

  • @dannapolitano9616
    @dannapolitano9616 9 ปีที่แล้ว +107

    matrix = bullet to my brain

  • @roninovereasy
    @roninovereasy 9 ปีที่แล้ว +219

    Matrices are the fundamental building blocks for building models. This is utilized in several aspects of data science including machine learning, statistics including regressions. And conceptually, it is hard. Anyone who thinks they are stupid are wrong (otherwise you wouldn't be watching these videos in the first place). Just keep plugging.

    • @IngaMitinyan
      @IngaMitinyan 9 ปีที่แล้ว +16

      +Fred Sanchious thanks for the encouragement!

    • @andrewmunnings4545
      @andrewmunnings4545 7 ปีที่แล้ว +5

      Fred Sanchious thanks for the encouragement

    • @metallisac
      @metallisac 7 ปีที่แล้ว +12

      Or people are learning this in the first place because they simply have homework. Fuck math lol

    • @brooke4603
      @brooke4603 6 ปีที่แล้ว +3

      i needed this

    • @aku7598
      @aku7598 3 ปีที่แล้ว

      It's confusing.
      Ax=b
      Sometimes A represent Vectors and x the weight.
      Sometimes A just scalar with x as a vector.

  • @jordanpayne8826
    @jordanpayne8826 5 ปีที่แล้ว +24

    This video literally couldve been two minutes but i still love you

  • @Starchildcasanova
    @Starchildcasanova 13 ปีที่แล้ว +10

    I don't see how anyone could dislike this video. I want you to know that this refresher is going to help me pass Mechanics class. Thank you.

  • @jg6551
    @jg6551 6 ปีที่แล้ว +69

    he starts solving with matrices at 12:00
    if you are here for a quick review go to 12:00

  • @GeForce1080
    @GeForce1080 5 ปีที่แล้ว +85

    2008: Nope
    2098: Nope
    2010: Nope
    2011: Nope
    2012: Nope
    2013: Nope
    2014: Nope
    2015: Nope
    2016: Nope
    2017: Nope
    2018: Nope
    2019:* Now is the time!!*

  • @Max47340
    @Max47340 ปีที่แล้ว +3

    I usually enjoy your videos, but on this one you bombed! I’m more confused than before 😮

  • @MSFR-911_
    @MSFR-911_ 3 ปีที่แล้ว +2

    سبحان الله وبحمده سبحان الله العظيم
    استغفر الله العظيم الذي لا إله إلا هو الحي القيوم و أتوب إليه
    سبحان الله وبحمده عدد خلقه ورضا نفسه وزنة عرشه ومداد كلماته
    اللهم صَلِّ وسَلّمْ عَلَى نَبِيْنَا مُحَمد ﷺ

  • @hypercube3495
    @hypercube3495 2 ปีที่แล้ว +2

    Khan academy is so legendary I was 3 years old when this video was published. I watched these in 5th grade I watched these in high school and now I’m watching these while taking calculus in college. It’s totally tripping me out that this video has been ready and waiting since around the time I learned to count to teach math in a way I understand thanks khan.

  • @MSFR-911_
    @MSFR-911_ 3 ปีที่แล้ว +3

    ورد عن رسول الله ﷺ: اللهم أنت ربي لا إله إلا أنت، خلقتني وأنا عبدك، وأنا على عهدك ووعدك ما استطعت، أعوذ بك من شر ما صنعت، أبوء لك بنعمتك علي، وأبوء بذنبي فاغفر لي فإنه لا يغفر الذنوب إلا أنت، من قالها حين يمسي فمات من ليلته دخل الجنة، ومن قالها حين يصبح فمات من يومه دخل الجنة

  • @rrrr-ij4zc
    @rrrr-ij4zc 4 ปีที่แล้ว +2

    43 years old and understanding this just now. What did I 'learn' in high school math and in math that I had in 1st year of university? Something like Sal's video would have save me a lot of trouble. Maybe I should feel grateful that I am understanding this at least now.

  • @rinnegansr5980
    @rinnegansr5980 5 ปีที่แล้ว +9

    "so this is stuff you should already know so well skip this" thanks maths professor even in the advanced books that super nerds used i couldnt find it.

  • @marcusantonius4121
    @marcusantonius4121 9 ปีที่แล้ว +9

    At my school we also have to use matrices to solve equations that simplify down to 0=0 i.e.
    2x+y=2
    4x+2y=4

  • @CreativiTimothy
    @CreativiTimothy 4 ปีที่แล้ว +3

    His handwriting really improved 10 years later lol. He wrote his -2 as -1 and his 3 as 2 at 14:28

  • @DrawingHeart
    @DrawingHeart 6 ปีที่แล้ว +117

    Anyone else hopelessly lost

    • @yeabsraamare6615
      @yeabsraamare6615 4 ปีที่แล้ว +2

      if this video is a bit confusing then you should join the channel " The Organic chemistry tutor" that dude is amazing like A++++

    • @ServitorSkull
      @ServitorSkull 4 ปีที่แล้ว +1

      Fear not friend. As long as there is math, we have hope.

  • @jiyoonpark5022
    @jiyoonpark5022 5 ปีที่แล้ว +10

    11 years have passed and still, there is no video that exceeds this one

  • @indistantdreams
    @indistantdreams ปีที่แล้ว +4

    old gold days. 240p videos. memories.

  • @OrthosWasTaken
    @OrthosWasTaken 6 ปีที่แล้ว +1

    My guy, you've probably got comments like these thousands of times but I'm on a fast track math class as I could never get my GCSE, as I found math to hard. But you for whatever reason are so intuitive to follow. Thank you for being one of the major reasons I'm going to university,

  • @TheAutumnWinter
    @TheAutumnWinter 14 ปีที่แล้ว +3

    Thanks so much! I got behind in class and failed a quiz yesterday on this subject. I have a test tomorrow on matrices and now I'm not worried about failing it! I'm a tactual learner, so being able to use steps makes it so much easier for me! You're a lifesaver!

    • @016abhirajpal9
      @016abhirajpal9 3 ปีที่แล้ว

      hey how are you today ? and how did your test go ?

    • @RohitKUMAR-np8qd
      @RohitKUMAR-np8qd 2 ปีที่แล้ว

      what are u doing now

  • @leechaloemtiarana7412
    @leechaloemtiarana7412 4 ปีที่แล้ว +40

    Who else is here at 1 am struggling?

    • @TheoryOfSnek
      @TheoryOfSnek 4 หลายเดือนก่อน +1

      11:37 for me as I’m typing this, but close enough

    • @NeemaPolodeous
      @NeemaPolodeous 2 หลายเดือนก่อน

      It's 1pm for me

    • @RobinSingh-yc4fo
      @RobinSingh-yc4fo หลายเดือนก่อน

      Me 😂at 2AM😊

  • @itoroessien6400
    @itoroessien6400 2 ปีที่แล้ว +2

    Discovering this 12 years after, this is a goldmine sir

  • @barbellbrat
    @barbellbrat 9 ปีที่แล้ว +32

    I have two more days till school starts, and a packet that I have to get at least B- to be accepted into AP Algebra II. I know everything in the packet, but guess what I don't know? Matrices, I spent literally 2 hours trying to figure out how to do this crap that I've never learned, and trying to learn it from 20 minutes of bullshit. Thank you.

    • @Alhussainba
      @Alhussainba 7 ปีที่แล้ว

      how did you do with the school ?

    • @jasonwalker6285
      @jasonwalker6285 6 ปีที่แล้ว

      How'd it go where you at now fam

    • @andywattanaskolpant8378
      @andywattanaskolpant8378 5 ปีที่แล้ว

      How'd it go?

    • @justsomeguy7921
      @justsomeguy7921 4 ปีที่แล้ว +1

      Don’t want to be repetitive of everyone else, but how did it go, and how are you doing now?

  • @mhonromopatton8068
    @mhonromopatton8068 3 ปีที่แล้ว +1

    Love how you can't stop thinking about The Matrix Movie while doing matrices..............Thanks alot for this free and valuable education SAL💖💖

  • @anjalipal3031
    @anjalipal3031 3 ปีที่แล้ว

    i’m in calc and i’d NEVER even heard of these until i was taking the pre-ACT a few weeks ago... thank god for khan academy

  • @jacob240694
    @jacob240694 11 ปีที่แล้ว

    Switching from an Architecture degree to aerospace engineering - these videos are making my life so much easier!
    Thanks!

  • @alyssabalabanova1918
    @alyssabalabanova1918 6 ปีที่แล้ว +2

    Thank you so, so, so much for these videos! I am doing a Masters degree and had to understand matrices for the underlying equations in statistics and if it was not for your videos, I might have given up! Thank you, you are amazing :)

  • @sledge2742
    @sledge2742 4 ปีที่แล้ว +1

    way better than any lecturer i've ever had

  • @sohibjondilmurodov6259
    @sohibjondilmurodov6259 9 วันที่ผ่านมา

    I love how he explains the applications as well

  • @andrewogden1480
    @andrewogden1480 10 ปีที่แล้ว +12

    Khan,
    I love you! I have been sitting in class for 2 weeks now and have never been more confused. Your videos always start off so basic that you can pick up any where in a subject.

  • @youneedlenny6542
    @youneedlenny6542 6 ปีที่แล้ว +46

    Yeet I have a math final tomorrow and I don’t know what I’m doing

  • @CYBERWIZARD
    @CYBERWIZARD 3 หลายเดือนก่อน

    This is so helpful even though I am in Algebra 2. Having multiple ways to double check myself, even though I can solve a system of equations with 3 variables through substitution and elimination is greatly useful.

  • @jrendoso
    @jrendoso 16 ปีที่แล้ว +1

    such a wonderful video, really helpful.
    i wonder how to do this whit a 3x3 or 4x4 matrix.

  • @andygarrido58
    @andygarrido58 11 ปีที่แล้ว +20

    lol Matrix movie reference 1:50

  • @IamThatGirlMegan
    @IamThatGirlMegan 12 ปีที่แล้ว

    you explain this better than anyone who has tried to teach me. Going to ace my test tomorrow!

  • @-hiandbye1994
    @-hiandbye1994 ปีที่แล้ว

    This is more helpful than my teacher trying to teach using Matrices to solve a system of equations.

  • @marokay3269
    @marokay3269 11 ปีที่แล้ว

    yay!!! now I can do my assignment....my brain was dead coz of not doing matrices in so long...its coming back to life. thank-you :)

  • @arbbra6837
    @arbbra6837 11 ปีที่แล้ว

    What does the ethics mean to you? This guy (Sal) has shared more than 3500 tutorials with no charge, I consider this as a high human value! By the way I think that today Sal is the synonim of the humanity and academism together!

  • @darksteel78
    @darksteel78 14 ปีที่แล้ว

    The only thing I can say is thank God my teacher taught me Cramer's Rule. I find it to be way simpler. You should make a video on it Sal if you haven't already. This method also gets the job done though.

  • @jaredgreathouse3672
    @jaredgreathouse3672 4 ปีที่แล้ว

    I now can really USE matrices in statistical applications, namely in regression analysis, command writing for Stata and for solving systems of equations

  • @carissa_f
    @carissa_f ปีที่แล้ว

    My homeschool book does a crappy job explaining any of these. Thank you for the help!

  • @KlaskeyProductions
    @KlaskeyProductions 11 ปีที่แล้ว

    This makes much more sense than the way my linear algebra professor taught it. This method of "examples now, prove later" works much better than its inverse, IMO. Maybe it's just me though.

  • @mastermix3000
    @mastermix3000 14 ปีที่แล้ว

    THANK YOU!!!!!!!!!!
    I SWEAR some people are just much better than teachers

  • @kartiksingh_1
    @kartiksingh_1 13 ปีที่แล้ว

    I want a world in which every teacher explains like you do

  • @FelipeZucchetti
    @FelipeZucchetti 8 ปีที่แล้ว +6

    Thanks Sal for your fucking awesome explanations...i hope one day to be able and pay you back for all free knowledge you share...I really appreciate your videos...already watched almost all calculus videos and now im starting linear algebra...you are a great teacher...thanks again...:)

  • @pittsburghguy2520
    @pittsburghguy2520 6 ปีที่แล้ว +3

    You actually made this harder than it already was, wow thats a first

  • @muntynz
    @muntynz 14 ปีที่แล้ว +1

    Love it, you are a fantastic teacher, no mono tone and you answer ALL my questions... Thank you for taking the time.

    • @RohitKUMAR-np8qd
      @RohitKUMAR-np8qd 2 ปีที่แล้ว

      @@heartcomedy5 hoping he's doing great

  • @fatima60326
    @fatima60326 ปีที่แล้ว

    I didnt get the visual represenation amd explaination of it despite the others in matrix series of video which was amazing so far

  • @BerPolo
    @BerPolo 14 ปีที่แล้ว

    Very nice tutorial. Definitely helps, teacher doesn't explain much.

  • @xiangyucheng-xn4sp
    @xiangyucheng-xn4sp 6 หลายเดือนก่อน +1

    -1in yellow should be -2

  • @PepperAddict
    @PepperAddict 12 ปีที่แล้ว

    Yes we all should have learned how to solve linear equations in middle school but now we are using linear equations as an example to learn how matrices are used to find the solution for hundreds of linear equations

  • @oazedlium2985
    @oazedlium2985 3 ปีที่แล้ว +1

    2:26 y= -3/2.x +7/2

  • @Killuminatismd
    @Killuminatismd 13 ปีที่แล้ว

    so proud to be a bengali. I look up to this man. We need men like him to further humanity :)

  • @nightwolfz
    @nightwolfz 14 ปีที่แล้ว +1

    Thanks for the videos!!! You're a life saver!!
    P.S. You could use windows journal, everything you write will look much cooler because of anti-aliasing, just change the paper color to black and disable vertical lines/margin.

    • @gamingverse8181
      @gamingverse8181 2 ปีที่แล้ว

      wow 12 years later and still helps

  • @tmgiesen
    @tmgiesen 7 ปีที่แล้ว +1

    You’re a very good teacher. Thank you.

  • @SakthiPandiSocialMedia
    @SakthiPandiSocialMedia 10 ปีที่แล้ว +1

    This really helped me for my math test! Thanks Sal!

  • @retzuaiga
    @retzuaiga 13 ปีที่แล้ว

    this refresh my memory, i need this for higher level courses

  • @CrewNDx
    @CrewNDx 3 ปีที่แล้ว

    Thanks for making me love maths without asking for even a single penny. you deserve the best in the world. Sal 💙

  • @SoloPro
    @SoloPro 9 ปีที่แล้ว

    It was a very nice video and I have learnt a lot in 1hour... I will probs try watch all of the playlist because its so easy to follow... Thanks sal

  • @jeffgalef121
    @jeffgalef121 7 ปีที่แล้ว

    Thank you so much for explaining the intuition behind this. I always found it shocking that you could find a vector that satisfies multiple equations, but your drawing of the intersection of lines made this very clear.

  • @Waranle
    @Waranle 16 ปีที่แล้ว

    Thank you alot Khan. Im going to take linear Algebra this fall.

  • @ludicrouslego2772
    @ludicrouslego2772 6 ปีที่แล้ว

    Omg this makes way more sense now! Thank you now I’m fully prepared for the test I’m taking soon.

  • @marokay3269
    @marokay3269 11 ปีที่แล้ว

    your such a khan academy student :D "some people learn at different paces"

  • @evalynns8530
    @evalynns8530 11 ปีที่แล้ว

    Thank you so much!!! The way my teacher described it had me so confused, but this makes so much more sense, and it's way faster! :D

  • @richardrampersaud6818
    @richardrampersaud6818 7 ปีที่แล้ว +2

    Thank you so much for this, it's so much clearer now!

  • @ibrahimmuhammad2339
    @ibrahimmuhammad2339 4 ปีที่แล้ว

    This was 11 years ago. Still helping people

  • @GndmMkv
    @GndmMkv 14 ปีที่แล้ว +1

    im going to show this in my class and amaze my teacher

    • @jcp2415
      @jcp2415 4 ปีที่แล้ว

      I hope they were impressed

  • @gerardopadilla9934
    @gerardopadilla9934 7 ปีที่แล้ว

    About to take my final in like 30 minutes this gonna help so much

  • @yugi3234
    @yugi3234 15 ปีที่แล้ว

    THANK YOU SO MUCH Awesome video my math teacher at school explained this horribly thank you for clearing it all up for me

  • @bituu_shukla
    @bituu_shukla ปีที่แล้ว

    Hello sir I'm watching your lectures ,from India ❤

  • @s8ntiago
    @s8ntiago 6 ปีที่แล้ว +3

    my algebra teacher didn’t help me with this at all 🤪 thank you so much

  • @babybeautified
    @babybeautified 13 ปีที่แล้ว

    See this is how young ppl in this generation can learn effectively.

  • @LAnonHubbard
    @LAnonHubbard 14 ปีที่แล้ว +1

    Nice one Sal.

  • @2OthCenturyFox
    @2OthCenturyFox 14 ปีที่แล้ว +4

    Thanks for the info, however you need to get some new software!

  • @kyoshintama
    @kyoshintama 12 ปีที่แล้ว

    having my exam in 2 hrs, this is really helping me study :)

  • @klblackstar
    @klblackstar 12 ปีที่แล้ว

    yes, there is. both of those methods will work.

  • @niocpn
    @niocpn 12 ปีที่แล้ว +2

    I fucking love salman khan, his voice teaches and soothes me, at the same time!

  • @andersonanjo5388
    @andersonanjo5388 2 ปีที่แล้ว

    lately your math calculations have been helping me alot. Thank you very much Sir.

  • @arshad589
    @arshad589 14 ปีที่แล้ว

    Thanks man, i have exams tomorrow, and i didn't know how to do that !!
    u really helped me....god drive you to heaven :P

  • @callmehandsomeB_4_24PM
    @callmehandsomeB_4_24PM 4 ปีที่แล้ว +2

    After 12 years I'm back!

  • @asianflex786
    @asianflex786 13 ปีที่แล้ว +1

    @RuudDude1 agreed. if you get bored of an expanation then maths isnt the course for you.

  • @AmzSongwriter007
    @AmzSongwriter007 12 ปีที่แล้ว

    rearrange it so it looks like -x + y = 4, then you can do the problem this way.

  • @electricfeel2012
    @electricfeel2012 15 ปีที่แล้ว

    you are the beast of math!!!

  • @a00000z100
    @a00000z100 11 ปีที่แล้ว +1

    I'm wondering about why did you add ( 6*7 ) + ( 2*6 ) at 15:06 . Why you did not subtract as the first one

    • @indiaparker3719
      @indiaparker3719 2 ปีที่แล้ว

      his hand writing was bad so its actually (6*7) + (3*6) but you are right he subtracted the first one which was (6*7) and (2*6) and he got thirty. i was super confused because i have not seen him do it that way so i think its a mistake.

  • @austinclark6418
    @austinclark6418 5 ปีที่แล้ว

    Your voice is so relaxing

  • @GenaEnSamIAm
    @GenaEnSamIAm 12 ปีที่แล้ว

    Couldn't agree more!!!! Nicely put!

  • @poisonpotato1
    @poisonpotato1 6 ปีที่แล้ว

    It helps a lot in mech engineering

  • @Gartonia
    @Gartonia 11 ปีที่แล้ว

    He knows everything. He looked into the Time Vortex. And the Time Vortex looked into him.

  • @veigar1235
    @veigar1235 2 ปีที่แล้ว

    another very valuable explanation.❤

  • @Kennychoco22
    @Kennychoco22 13 ปีที่แล้ว

    I understood everything except in the end when we don't do anything with the 1/30. i get it when we multiplied the matrices in the end but we didnt with 1/30

  • @Johan-st4rv
    @Johan-st4rv 7 ปีที่แล้ว

    I am in Calculus III and found this to be quite complicated no idea how I managed to get it all the way back in Precalculus

  • @friskkyy21
    @friskkyy21 12 ปีที่แล้ว

    i love this guy man!.... God bless you khan :D

  • @lancelindlelee7256
    @lancelindlelee7256 10 ปีที่แล้ว

    Thanks. Another time this is useful is when you are allowed to use a calculator. My calc can do a 4x4 matrix but only 3 systems of equations

  • @feitingschatten1
    @feitingschatten1 12 ปีที่แล้ว

    Just a little extra, there's a free book by Jim Hefferon, who also teaches the cool easy stuff first. It's a good text (as it's free in pdf) to go along