Gaussian Elimination & Row Echelon Form

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  • Опубликовано: 6 июл 2024
  • This precalculus video tutorial provides a basic introduction into the gaussian elimination - a process that involves elementary row operations with 3x3 matrices which allows you to solve a system of linear equations with 3 variables. You need to convert the system of equations into an augmented matrix and use matrix row operations to write it in row echelon form. Next, you can convert back into a system of linear equations and solve using back substitution.
    Full-Length Math & Science Videos:
    / collections
    ___________________________________
    Introduction to Matrices:
    • Intro to Matrices
    Adding and Subtracting Matrices:
    • Adding and Subtracting...
    Scalar Multiplication of Matrices:
    • Scalar Multiplication ...
    Solving Matrix Equations:
    • Solving Matrix Equations
    Multiplying Matrices:
    • Multiplying Matrices
    __________________________________
    Gaussian Elimination & Row Echelon Form:
    • Gaussian Elimination &...
    Gauss Jordan Elimination:
    • Gauss Jordan Eliminati...
    Gaussian Elimination With 4 Variables:
    • Gaussian Elimination W...
    Inverse of a 2x2 Matrix:
    • Inverse of a 2x2 Matrix
    Inverse of a 3x3 Matrix:
    • Inverse of a 3x3 Matrix
    __________________________________
    Determinant of 2x2 and 3x3 Matrix:
    • Determinant of 3x3 Mat...
    Determinant of 4x4 Matrix:
    • How To Find The Determ...
    Cramer's Rule - 2x2 Linear System:
    • Cramer's Rule - 2x2 Li...
    Cramer's Rule - 3x3 Linear System:
    • Cramer's Rule - 3x3 Li...
    ___________________________________
    Final Exams and Video Playlists:
    www.video-tutor.net/

Комментарии • 803

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Год назад +37

    Final Exams and Video Playlists: www.video-tutor.net/
    Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
    Next Video: ruclips.net/video/eYSASx8_nyg/видео.html

  • @droomahbroo9291
    @droomahbroo9291 2 года назад +682

    This man carried me through 1st year and now hes carrying me through honours as well. You are a true legend!

    • @aimokoivunen4787
      @aimokoivunen4787 2 года назад +13

      Best of luck!

    • @master_baiter1873
      @master_baiter1873 Год назад +6

      His exapmles are ass though. He picks the easiest examples. He could give a harder one.

    • @droomahbroo9291
      @droomahbroo9291 Год назад +17

      @@master_baiter1873 well he’s not going to do ypur homework for you :D. I usually watch the video to learn the basic concepts and then go through the examples and exercises given in class. I then use his examples to boost my confidence the morning of the test. Seems stupid but its gotten me through Physics 5 so…

    • @master_baiter1873
      @master_baiter1873 Год назад

      @@droomahbroo9291 i mean he could give one hard example. He chose easy examples. Ones i can easily do in my head.

    • @GoToMan
      @GoToMan Год назад +2

      @@master_baiter1873 I suggest you pick up Strang's linear algebra

  • @jasonchen3507
    @jasonchen3507 3 года назад +2047

    This guy explains it so well...my textbook explains it like a brick.

  • @mrguys2822
    @mrguys2822 Год назад +806

    Your videos are so much easier to understand than my lectures. Thank you for carrying me through university xD

    • @amreenaym786
      @amreenaym786 Год назад +22

      Y’all are learning this in uni? Bro I’m having a hard time understanding this and I’m a freshman in hs

    • @higgsboson6274
      @higgsboson6274 Год назад +19

      @@amreenaym786 just keep going, keep practicing. things will make sense eventually

    • @suraboss2673
      @suraboss2673 Год назад +5

      @@amreenaym786 its literally going to be easy learning this in university

    • @josiahscarrmusic6750
      @josiahscarrmusic6750 Год назад +12

      @@amreenaym786 you do repeat stuff to regain that familiarity, though I am learning this cause I have a maths module as part of my CS degree

    • @oluwakoredeonasanya3267
      @oluwakoredeonasanya3267 Год назад +9

      @@amreenaym786 in my country we don't learn this stuff in high-school, so I'm learning this for the first time in university

  • @israel4101
    @israel4101 5 лет назад +252

    This RUclips channel is literally my first year of my BSc's saving grace. I can't thank you enough.

    • @KingNat.
      @KingNat. 4 года назад +21

      Not even first year bruh, you can use some of this stuff for second year too. This man got me through calc in first year CS

    • @youssefbayoumi2694
      @youssefbayoumi2694 3 года назад

      can i minus 2 rows ?? someone answer plz

    • @PenandPaperScience
      @PenandPaperScience 3 года назад

      @@youssefbayoumi2694 What exactly do you mean? You can indeed add a row with minus 2 times another row.

    • @icebearreal
      @icebearreal 2 года назад +2

      @@PenandPaperScience Hi! I am one of your subs.

    • @icebearreal
      @icebearreal 2 года назад +2

      @@PenandPaperScience I'm glad to find you here.

  • @kastriotselimi7444
    @kastriotselimi7444 Год назад +43

    I have an exam tomorrow,and I’ve been trying to learn this from scripts of my teacher for 3 hours and there is a guy like you that teach me all the stuff for 18 minutes.I wish you a good health and life.Thank you

  • @tenyshaross-vanmierlo7163
    @tenyshaross-vanmierlo7163 6 лет назад +60

    This youtube channel is literally my first year of my BSc's saving grace. I can't thank you enough.

  • @kipiekiee519
    @kipiekiee519 10 месяцев назад +11

    I just wanna say, you've helped me so much over the past year. Precalc, calc 1, a calc 2 crash course over the summer, and now linear algebra. I doubt i'd of been able to understand everything as much as I do now without your videos helping us walk through each new method and idea. Thank you for taking the time you have to help us learn

  • @ddahstan6876
    @ddahstan6876 2 года назад +100

    One of the most humble educators that we're blessed with!
    A heartfelt Respect to your dedication and patience because a lot of us will survive much longer in math, or even feeling more motivated!! 🍭

    • @AFCOE
      @AFCOE Год назад

      What I wonder is that his title is chemistry tutor😂😂😂. But teaching math more than math teachers😅😅😅😅

  • @mosessydneyruiz87
    @mosessydneyruiz87 3 года назад +552

    I am here because of the online class. Self-study huhu. Like also if this is your case! Goodluck to all of us!

  • @taekwondotime
    @taekwondotime 5 лет назад +721

    This seems to be a common misunderstanding with matrices. *Echelon form is simply the final matrix after you've finished Gauss elimination* . (The matrix at 6:10.) It need only have 0's in the lower left-hand corner. *There is no requirement to have 1's along the main diagonal because they do not help in solving the problem* . They are simply wasted operations and are not done in practice. (Unless you want to do Gauss-Jordan elimination... which is also not used in practice.)
    People seem to confuse the two. You only need 1's on the main diagonal if you're prepping for Gauss-Jordan elimination which then transforms the numbers in the upper right corner of the matrix to 0's as well. If you're not doing Gauss-Jordan, then don't worry about having 1's.
    *Once you obtain the matrix @**6:10**, then we know that 4z = 8 and therefore z = 8/4 = 2* . From there we use back substitution to solve for the remaining variables.
    FYI: This is straight out of my math textbook if you don't believe me.
    *Source: Advanced Engineering Mathematics by Erwin Kreyszig*

    • @taekwondotime
      @taekwondotime 5 лет назад +41

      TIP: The *scale* operation is your friend! As soon as you start getting into non-trivial matrices where the coefficients don't eliminate nicely, use the scale operation to get them up to a common value and then eliminate them. This helps you avoid ugly fractions and awful decimal numbers that have infinite precision.
      For example, consider the following system of equations:
      x + y - z = 9
      8y + 6z = -6
      -2x + 4y - 6z = 40
      Without using the scale operation, you'll hit a wall by about step 3.

    • @pablonapan4698
      @pablonapan4698 5 лет назад +5

      Thanks

    • @dami4271
      @dami4271 5 лет назад +18

      @@taekwondotime so whats the scale operation

    • @WTHnada
      @WTHnada 5 лет назад +7

      You should have explained that in the video I was so confused :(

    • @alsudairy.k5647
      @alsudairy.k5647 5 лет назад +29

      The one he did is called Reduced Row Echelon form.

  • @MARIN-py9ye
    @MARIN-py9ye 3 года назад +11

    My prof. explained this to me 3 times and I didn't get it, watched your video one time and figured it out instantly. Perfect job on the tutorial, thank you!!!

  • @EmilyBrownn
    @EmilyBrownn 3 года назад +64

    I am in maths major and this year is my second year in this department. Before online education, I was learning with your videos. Actually my college is very hard but you solve easy question,so I love your videos, because I feel like I am a paradox in class of my teachers. It is very awful situation. I am so glad to discover this channel thanks the organic chemistry tutor

  • @EPICGamer516
    @EPICGamer516 2 года назад +24

    You currently are my savior for taking linear algebra! Thank you for doing such great work for the world!

  • @dania8183
    @dania8183 4 года назад +5

    A THANK YOU COMMENT IS NEVER ENOUGH TO YOU GUYS!!!! LIFE SAVERS!!! THANK YOU VERY MUCH TEACHER, THE ORGANIC CHEMISTRY TUTOR.

  • @georgesadler7830
    @georgesadler7830 2 года назад +9

    MR. Organic Chemistry Tutor, this is an excellent introduction to the Gaussian Elimination Method and Row Echelon Form in classical Linear Algebra. Linear Algebra is very useful in different levels of mathematics.

  • @jackdeily8615
    @jackdeily8615 4 года назад +960

    My brain does not let me do this. I have been trying so hard for a week and I feel like my head is going to explode.

  • @joanhewitt-fagan2815
    @joanhewitt-fagan2815 5 лет назад +22

    thanks. you are absolutely the best, my math teacher totally confused the class with this principle.

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    @kreedapanda7741 5 лет назад +52

    I wish this guy was my math lecturer.

  • @aimokoivunen4787
    @aimokoivunen4787 2 года назад +13

    Felt so lost after my professor taught this. Came here for help as always. Was not disappointed. You're a good man. Thankyou

  • @azizalaliq8
    @azizalaliq8 5 лет назад +26

    This RUclips channel is literally my first year of my Beng's saving grace. I can't thank you enough.

    • @CptMaahir
      @CptMaahir 3 года назад

      Did you find his thermodynamics vids helpful?

  • @thedrumminggamer1064
    @thedrumminggamer1064 9 месяцев назад +3

    your videos are 10x more informative than any lecture i have sat , keep up the good work

  • @dianaingato3067
    @dianaingato3067 5 лет назад +6

    This just saved me.. I got my end of semester exam on Tuesday.. Hope this is going to help a big deal. Thank you.

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    @hybe8459 2 года назад +19

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  • @lovelya72
    @lovelya72 Год назад +2

    Thank you so much for the explanation! I can't understand this in my textbook and all and you only took 20 minutes for me to completely understand this concept!

  • @emilytran212
    @emilytran212 5 лет назад +4

    You've never failed me. I love you so much!

  • @hcxmedi3000
    @hcxmedi3000 3 года назад +1

    Your a legend. The way you teach. I learn everything from you.

  • @sukhoiboy4140
    @sukhoiboy4140 2 года назад

    ive been a university student for 3 years now. Organic chemistry tutor is awesome! I remember the morning of a Calc two exam, other students asking how each other felt... I told them i reviewed some organic chemistry tutor videos their jaws dropped!!! hahaha. they didnt realise u did math lol. I love you man keep it up!

  • @ejuramusic
    @ejuramusic 3 года назад +2

    You are a saint! I just realized I forgot to do two math assignments and I needed to learn how to do this immediately

  • @user-rv4zm8xm1d
    @user-rv4zm8xm1d 4 года назад +8

    You made this so much easier ! Thank you!

  • @NotEnoughAlpacas
    @NotEnoughAlpacas 2 года назад +2

    He has been my saving grace in 5 different classes so far

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  • @jamesmunroe6558
    @jamesmunroe6558 7 месяцев назад +1

    Simple, clear, and self-evident. Many thanks!

  • @undinesoul5261
    @undinesoul5261 3 года назад +7

    dude, you're awesome, thanks so much, I was really struggling with this and this video has helped me so much. def gonna buy some merch

  • @timothylittlefield
    @timothylittlefield 2 года назад +44

    You corrected both z=2 and -2 in the top row. Great job and thank you! I can solve variables using Gaussian elimination.

    • @dazzlingforests1373
      @dazzlingforests1373 2 года назад +7

      Thank you for writing that he caught that! I was getting worried lol

  • @user-sc4ds3dw4b
    @user-sc4ds3dw4b 2 года назад +9

    this guy is responsible for me to pass by engineering . thank you

  • @joshryanbligh5791
    @joshryanbligh5791 3 года назад +1

    Thank you for the vid! Explained it far better than my instructor did!

  • @ez5267
    @ez5267 3 года назад +66

    We have an exam tomorrow, including this topic. Hoping to pass it.

    • @neilialopez7446
      @neilialopez7446 3 года назад +1

      I have one tomorrow too cri.

    • @ahmetkarakartal9563
      @ahmetkarakartal9563 3 года назад +1

      @@neilialopez7446 ahahaha me too

    • @tarylee357
      @tarylee357 3 года назад +2

      updates? how was it! im having one soon :)

    • @PenandPaperScience
      @PenandPaperScience 3 года назад +3

      Hope it went well. And for those students out there that want some more practice on Gaussian Elimination, I've made a video where I solve such exercises step-by-step. It might help some :)
      ruclips.net/video/nyWp9sr8uGE/видео.html

    • @StevesUniverse
      @StevesUniverse 3 года назад

      UPDATE??

  • @MoiraBrady
    @MoiraBrady Год назад +3

    Thank you. You explained it so well and now I can practice this till I can do it without help. Really helpful and you have taken the stress out of my weekend :)

  • @JhunsTV
    @JhunsTV Год назад +1

    This channel really is the best it could really relay the gist to it's viewers, those professor just make my life harder and complicated

  • @expansivegymnast1020
    @expansivegymnast1020 3 года назад +3

    I will pass my Discrete Math class because of you. Thank you so much!

  • @BigBrother4Life
    @BigBrother4Life 5 лет назад +639

    They always do the easiest question on the internet.

    • @TheGunzSkido
      @TheGunzSkido 5 лет назад +31

      well you only need the basic anyways for this kind of question.

    • @dabigboom2426
      @dabigboom2426 5 лет назад +39

      @@TheGunzSkido Naaw bro im in Algebra 2 and my questions are hard af

    • @TheGunzSkido
      @TheGunzSkido 5 лет назад +19

      @@dabigboom2426 keep learning bro. You can do it

    • @canerc6668
      @canerc6668 4 года назад +10

      Otherwise we could be afraid of how difficult it may be : )

    • @ashleybellinghoven2331
      @ashleybellinghoven2331 4 года назад

      Ahmed01 I know !!!

  • @shereeannrichards3901
    @shereeannrichards3901 2 года назад +16

    You made this so easy to understand and follow. For days I have been losing my sanity trying to complete my assignment on this topic. Thank you

  • @paulvanbrakel
    @paulvanbrakel 9 месяцев назад +32

    For the people that get confused at 10:50: 'R3 = R1-R3 is the same as 'R3 = -R3 + R1. He writes it in a different way, but you're still working on 3R in both cases

    • @parthbhanushali9382
      @parthbhanushali9382 8 месяцев назад

      thanks a ton mate

    • @muhammedowais8541
      @muhammedowais8541 7 месяцев назад

      Thanks man now i think i understand.

    • @sreekumarnair-rl2wo
      @sreekumarnair-rl2wo 6 месяцев назад

      I don't understand it why it's R3=-R3+R1 we can directly go with R3=R3-R1 isn't it? Please help me with this

    • @oimatesimro2088
      @oimatesimro2088 6 месяцев назад

      @@sreekumarnair-rl2wo i think its because you have to write the ending row (R3) at the end of your operation, he explained it in another matrix vid, i think its the row operation vid

    • @ckaamuli8182
      @ckaamuli8182 2 месяца назад

      @@oimatesimro2088 wouldn't R3 = -R1+R3 work then?

  • @computersciencewithpeter
    @computersciencewithpeter 2 года назад

    Love how you exemplified all the concepts...

  • @lawrencemacharia3401
    @lawrencemacharia3401 Год назад +12

    Love how he explains everything in such a short time and detailed

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    @fafiethamae 3 месяца назад +1

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  • @jinxinchan7981
    @jinxinchan7981 4 года назад +2

    Thanks. I am taking this class online this summer term. Reading the material for 19 times, I still doesn't understand. Now... there is hope :)

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    @hiwotberhanu3814 4 года назад +60

    He "in this vedio"
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      @kopanokatebela8842 3 года назад +4

      That is the feeling i always get, i even know before opening the video that it is him because of the colours he love using..

  • @apheniesinegal2287
    @apheniesinegal2287 4 года назад +1

    I love this RUclips channel it helps and explains better than my professor

    • @OninabResources
      @OninabResources 4 года назад

      Get more on Gaussian elimination method of solving systems of equations from this link
      ruclips.net/video/eXHOytiWWAw/видео.html

  • @williesolomon614
    @williesolomon614 2 года назад +1

    Impressive explanation. You're genius, I SALUTE you sir. Thank you and God bless.

  • @ryankeshet5820
    @ryankeshet5820 4 года назад +1

    Why are you so helpful all the time?

  • @stephendemaine1426
    @stephendemaine1426 2 года назад

    Oh man, this just smacked me in the face, in a good way. Great breakdown. I am embarrassed to admit how much time I wasted with other resources before coming to this channel. I won't make that mistake again. Thanks for the insight!!

  • @sandismike3822
    @sandismike3822 Год назад

    The best tutor I've ever met....thank you sir

  • @josephkumwenda88
    @josephkumwenda88 Год назад

    Thanks man, this is helpful. You have saved my semester

  • @cometolearn8598
    @cometolearn8598 2 года назад +1

    Your a genius Keep going also you explain better than all my teachers :) 👏👏👏👏👏

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    This guy and kahn, legends.

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    @mervynsookun5995 Год назад

    You are a Pele or Maradona of a professor. Gifted genius !

  • @lindamanas954
    @lindamanas954 8 месяцев назад

    Beautifully explained. Thank you. You are a fantastic teacher! I have watched a few of your matrices videos. I am a Maths teacher myself but I wanted to revise Gaussian elimination!
    Linda in the UK

  • @joanieLeventis3077
    @joanieLeventis3077 11 месяцев назад

    I wish that I knew about this video while I was taking calculus in the university. It would have made things so much easier!!

  • @bigphuc
    @bigphuc 10 месяцев назад

    Doing the lords work with this video, awesome explanation!

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    @devOmarAZ 4 года назад

    From Egypt>>>>
    Thanks ..... Your The Best : )

  • @jasonsavard2819
    @jasonsavard2819 Год назад

    absolutely legendary ass guy. i cant believe im actually understanding everything clearly

  • @mr.creepz
    @mr.creepz Год назад

    thanks bro you made me understand this topic in just 20 mins while my teacher was teaching it from 2 months

  • @MsAlarman
    @MsAlarman 2 года назад

    Excellent explanation! A ton of patience !

  • @BigBlob7
    @BigBlob7 9 месяцев назад

    This was fantastic, completely lost in lectures but this is great!

  • @caseysun8868
    @caseysun8868 2 года назад +1

    Thanks so much!! My final exam includes this content, I've forgot for a long time though. Hoping to pass!!

  • @mathiasallon8368
    @mathiasallon8368 Год назад

    You really help me ...great teacher who I loves your tutorials

  • @PreferableFlavor
    @PreferableFlavor 4 года назад

    You are a god sent. Thank you for your easy to pick up informative videos

    • @OninabResources
      @OninabResources 4 года назад

      Get more on Gaussian elimination method of solving systems of equations from this link
      ruclips.net/video/eXHOytiWWAw/видео.html

  • @abugslife2461
    @abugslife2461 3 года назад +2

    let's gooooo linear algebra!! i passed calc 1 because of you!!!!

  • @sophiaonyoutube
    @sophiaonyoutube Год назад

    Awesome tutorial. Thank you so much!

  • @iUmairBilal
    @iUmairBilal 4 года назад +1

    Thank you so much sir !
    your videos helped a lot many times.
    I am very thankful to you.
    keep doing good work.

    • @OninabResources
      @OninabResources 4 года назад

      Get more on Gaussian elimination method of solving systems of equations from this link
      ruclips.net/video/eXHOytiWWAw/видео.html

  • @abdulasad8348
    @abdulasad8348 2 года назад

    Passed my math exam coz of you. Thanks a ton :))

  • @masterchi3ff
    @masterchi3ff Год назад

    Thanks brotha for the assist, helped me through numerical exams 🙏❤️

  • @user-oz2ei2qo7r
    @user-oz2ei2qo7r 3 месяца назад +1

    I had a hard time solving this but thanks to you it’s much easier 🎉

  • @kokopoppan
    @kokopoppan 3 года назад

    Nice vid soothing voice, maybe I will pass my test in 1 day :)

  • @Pinal375
    @Pinal375 Год назад

    Thanks very much for such a good explaination. good work and hope to continue watching your new videos.

  • @vascogomes2395
    @vascogomes2395 2 года назад

    Finally I learn this! Thanks a lot!!

  • @yayraatadja153
    @yayraatadja153 Год назад

    this guyyyyyyyyyyyyyyyy......from saving me weeks to exams to helping me finish entire courses before midsem

  • @normanhenderson7300
    @normanhenderson7300 Год назад

    I have not yet been acquainted with a video on this subject as yet that teach this method in a clear and systematic way. This one included.

  • @The_GreenHub
    @The_GreenHub Год назад

    Bro it straight up WORKS. You gotta like a video that can explain A-Level maths to a 14 year old.

  • @nightfox1416
    @nightfox1416 Год назад +4

    Great video! Only advice would be explain what you can do to simplify the matrix into row echelon form. For anyone watching, these are
    1) You can swap the rows (you CANNOT swap the columns)
    2) You can multiply the rows by any constant (in a similar way you would when solving simultaneous equations normally) except zero
    3) you can add or subtract one row from the other (you see this often in this video)

    • @inarvii8181
      @inarvii8181 Год назад +1

      I am a bit confused as to why in the second example, he did R1-R3. Why would it not be R3-R1 so that it is 2-2?

    • @sonu1747
      @sonu1747 Год назад

      @@inarvii8181 correct

  • @Thialeth
    @Thialeth Год назад +2

    i finally understand! thanks!

  • @gioqutaisi2wwq
    @gioqutaisi2wwq 4 года назад +1

    thank you from Georgia

  • @rashidissa5887
    @rashidissa5887 3 месяца назад

    Jack, me longer than a week, but have not lost hope. Never did matrix in my O-Level I am gradually catching up. Imagine in my late 70's, but still pursuing maths. I love it

  • @bequerhernandez8487
    @bequerhernandez8487 4 месяца назад

    I don’t even need to know this yet I scan understand it so well. Your goated.

  • @musebeonyango8958
    @musebeonyango8958 2 года назад

    You're my lecturer 100%💪💪good work

  • @shelematesfaye6672
    @shelematesfaye6672 5 лет назад +2

    thanks for support to me online eduction my teacher of algebra

  • @rehvjustins
    @rehvjustins 3 года назад

    Thank you! Better than solving it one by one.

  • @tebohomota5884
    @tebohomota5884 9 месяцев назад +1

    your videos could save me tomorrow !

  • @jessawatipachavula7852
    @jessawatipachavula7852 Год назад

    This video has really helped me, all thanks to you

  • @slimycat_ogbedrock
    @slimycat_ogbedrock 6 месяцев назад

    I learned this back in Middle School, but I forgot this was of doing it. Thanks.

  • @jameswatkins7747
    @jameswatkins7747 Год назад

    found it easier than my tutor explaining, awesome

  • @topfootball8211
    @topfootball8211 3 года назад +5

    I come here after class and understand everything clearly.This guy is such a helper

  • @blank5160
    @blank5160 Год назад

    Damn this video is life-saving!

  • @justrandom3849
    @justrandom3849 2 года назад

    Thanks so much for this video
    Very simple and clear

  • @bassitirfan7446
    @bassitirfan7446 Год назад

    Thanks for this , it helped me out a lot

  • @everythingbeautiful704
    @everythingbeautiful704 5 лет назад +3

    Thank you for this ,
    I have an exam
    And this so diffcult for me
    😞
    Now i understand
    🌹

  • @firaoltilahun3073
    @firaoltilahun3073 Год назад

    Wow u explain it in a simple way. Keep it up