Inverse of 3x3 matrix

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  • Опубликовано: 21 ноя 2024

Комментарии • 988

  • @lovesecretangels
    @lovesecretangels 5 лет назад +78

    Bro idk how many videos Ive watched trying to explain this to me.... I finally understand because of you, thank you 😭🙌🏻

  • @zonamade3380
    @zonamade3380 8 лет назад +332

    i thought this video was ending like four times until he kept going..

    • @JuliaChang
      @JuliaChang 6 лет назад +7

      i was praying in every second "god pls stahp now" but no.

    • @Minh-fo5fd
      @Minh-fo5fd 4 года назад

      @@JuliaChang wdym

    • @Osmosis-jy6xp
      @Osmosis-jy6xp 3 года назад

      @@Minh-fo5fd he means the video was so long that he was praying to god that it would end soon because the steps are tedious.

    • @Minh-fo5fd
      @Minh-fo5fd 3 года назад

      @@Osmosis-jy6xp ik i was messing with him

    • @Minh-fo5fd
      @Minh-fo5fd 3 года назад

      @@Osmosis-jy6xp or her

  • @julian7719
    @julian7719 9 лет назад +60

    Thank you, sir. You have saved me at least 3 hours of studying.

  • @terminatortscc1
    @terminatortscc1 9 лет назад +731

    This is exactly how teacher's are supposed to teach, obviously they don't otherwise i won't be here.

    • @christellemathieu179
      @christellemathieu179 7 лет назад +1

      Bestivitiness right

    • @lilrosiecheeks2143
      @lilrosiecheeks2143 6 лет назад +2

      Tbh

    • @smin4089
      @smin4089 6 лет назад +14

      When the govt takes control of anything, it goes to shit because the govt doesn't need to respond to market/human demands that are constantly changing.
      The private companies/mom&pop/free market is built on responding to the needs of the people/customers.

    • @sajjankumar2399
      @sajjankumar2399 6 лет назад

      ruclips.net/video/t7VHbC2_fTI/видео.html

    • @sajjankumar2399
      @sajjankumar2399 6 лет назад

      jungle305 ruclips.net/video/t7VHbC2_fTI/видео.html

  • @Rob-Herrera
    @Rob-Herrera 10 лет назад +661

    thats a lot of work for a freaking inverse

    • @MadOrange644
      @MadOrange644 10 лет назад +30

      It's simpler than that, but this video is fucking confusing.

    • @hstera
      @hstera 10 лет назад +7

      ***** lol, i agree. This method isn't that hard, and can be done relatively easy with the mentioned steps and some training... That being said, computers are extremely efficient at solving these kind of problems, so there is no point in learning the mechanics of solving them if they're larger than 3x3

    • @arvinroidoatienza7082
      @arvinroidoatienza7082 6 лет назад +3

      Actually, in my case its much easier. in our case, we used to do rref in finding the inverse. and its damn long, especially for 3x3 s.

    • @gytisdramblewolfskis8521
      @gytisdramblewolfskis8521 6 лет назад +3

      this is quite easy and not complicated. But there's a decent amount of shit to remember.

    • @oida10000
      @oida10000 6 лет назад +7

      There are two other methods: Gauss-Jordan elimination and Montante's method check them out here (they are there along with the video method):
      matrixcalc.org/en/#%7B%7B1,2,3%7D,%7B0,1,5%7D,%7B5,6,0%7D%7D%5E%28-1%29
      I watched the video because In was told that the method would be quiet fast for triangular matrices with many zeros (the nice thing about triangular matrices is that their determinate is simply the product of their diagonal (and you can transform a matrix into an equivalent triangular matrix using Gauss)) in the none zero part (like:
      (1 0 0 2)
      (0 1 0 0)
      (0 0 1 7)
      (0 0 0 1)
      but I don't see it yet.)

  • @tstone9151
    @tstone9151 8 лет назад +36

    Holy Crap Dude. Honestly thank you so much. My preCalc teacher explained it in a totally complicated way. You made it so simple for me

  • @rsilvas123
    @rsilvas123 9 лет назад +29

    Great video. Thank you for the step by step lesson. This is exactly what I needed.

  • @ari_says
    @ari_says 8 лет назад +1

    This was EXTREMELY helpful! My professor only went over 2x2 matrices, but our study guide includes 3x3 matrices also. You have saved my exam tomorrow!

  • @frymybaconpl0x
    @frymybaconpl0x 10 лет назад +258

    .......im colorblind

    • @philw5699
      @philw5699 9 лет назад +13

      Kevin Bacon I think they have glasses for that now.

    • @wesleyrichardson4940
      @wesleyrichardson4940 8 лет назад +11

      +Kevin “XDG 2014” Bacon Theres a way to get rid of that of lessen the effects. Its called rubbbing shit in your eye, very effective and not costly at all.

    • @moarts3733
      @moarts3733 6 лет назад +25

      go to your eye settings

    • @garveziukas
      @garveziukas 6 лет назад +8

      You should turn off the color blind mode in your display settings

    • @Muhammad-bf2dk
      @Muhammad-bf2dk 5 лет назад +2

      Did you put it in rice

  • @littleguydb2
    @littleguydb2 6 лет назад

    You are a lifesaver. Its almost as if college finite teachers teach this in the most complicated way possible for no reason. always trying to make us use the damn identity matrix like nah fam yall tweakin. Thank You again

  • @jeffreystevens8042
    @jeffreystevens8042 8 лет назад +71

    way to make me have an existential crisis at the end dude

    • @Matt_Lifts
      @Matt_Lifts 7 лет назад +3

      Yeah the ending made me laugh hahaha

  • @sppart1185
    @sppart1185 3 года назад

    Wow, you're video is quite the one... I can't believe I learnt over 5 periods in school to finally be able to find the inverse of a matrix (and still couldn't do it better) and you just did it in less than 15 minutes.... Thank you thousand times...

  • @saritar8819
    @saritar8819 10 лет назад +17

    Absolutely love this! You simplified it! And I love the sarcastic note at the end ;)

  • @emmanuelhoustonkwashie9222
    @emmanuelhoustonkwashie9222 6 лет назад

    This guy deserves my Professor's pay check every month for 60 years. This is the best way to teach students but some Professors take delight in failing students so they don't even care teaching it wrong. I love this video.

  • @C1001t
    @C1001t 8 лет назад +4

    Thank you very much. My lecturer explained it in a more complex way. This makes it so much easier. Finally have hope of passing this module: D

  • @sanjays9080
    @sanjays9080 8 лет назад

    the best teacher EVER ON RUclips!!!

  • @GDInspirations
    @GDInspirations 8 лет назад +114

    This makes me give up on life ! That congratulations at the end ....

    • @shgofftabibi7980
      @shgofftabibi7980 7 лет назад +4

      See the other video called A-1 in 60 seconds so easy

  • @fousin3391
    @fousin3391 2 года назад

    Only good, consistent explanation i could find

  • @SkPnDoWnStAiRs
    @SkPnDoWnStAiRs 11 лет назад +3

    Thank you! Honestly, this is much easier for me than using Row operations

    • @woodchuk1
      @woodchuk1 Год назад

      You’re not alone…I HATE using row operations, because I can never get the numbers to give me the identity matrix. I get it right in one place and it screws up somewhere else. This method always works without any of that nonsense, even if it takes longer. The Gauss Jordan process is about as useful as a screen door on a submarine if you’re doing this by hand.

  • @angeliquaserenity5009
    @angeliquaserenity5009 4 года назад +2

    Nice methodology! Your system of multiplying inverse matrices is much more simple than what I was originally taught. Thanks!!!

  • @yaraa.eldosoky2283
    @yaraa.eldosoky2283 7 лет назад +3

    This method is much easier than the ones I knew in the past and fastest ....... so thanks a lot👌🖒🖒

  • @sinepsinep123
    @sinepsinep123 5 лет назад

    Many thanks from Germany! Searched for a proper video which explains the whole process and in every video I watched anything missed, so I always had sign mistakes or wrong numbers.

  • @cjracer1000
    @cjracer1000 9 лет назад +11

    This method is completely unintuitive, but it works and that's all that matters. You explain every step. There are no arithmetic or logical leaps made and therefore there's no ambiguity or need for question. Your videos are literally perfect. You make patrickJMT look like garbage as he skips steps and I'm forced to do arithmetic on my own as if it's trivial. Well if it's so trivial then just do it. You do it! Thank you very much for being thorough and exhaustive. As far as I'm concerned, this is the only video on this topic.

  • @brianomarion
    @brianomarion 6 лет назад

    I know its years down the line since this video, but i swear you just saved my dumb brain all the stress of not getting what our eacher was doing,

  • @jessicajolly7828
    @jessicajolly7828 8 лет назад +4

    Very helpful! I am taking an R class and they are asking me to do inverses' of matrices, and I had NO idea what it was.

  • @MadFoxRemixed
    @MadFoxRemixed 6 лет назад

    still helpful 6 years later, you rock dude!

  • @tactic1313
    @tactic1313 4 года назад +15

    I dont get the part where you just multiply with "+" and "-" to the solved det from N
    is it always starting with a plus and then just + - + - + - ? also for a 4by4 matrix?

    • @woodchuk1
      @woodchuk1 3 года назад

      + - + -
      - + - +
      + - + -
      - + - +
      That’s the configuration for a 4x4. It alternates signs between entries in the row, but the initial entries in the rows also alternate signs going down the columns.

    • @tactic1313
      @tactic1313 3 года назад

      @@woodchuk1 thanks ! I managed to pass my exam but this will surely help others in the future ! 😁

  • @udarajayawardena2018
    @udarajayawardena2018 4 года назад +1

    Clean & Clear! Thank you Math Meeting

  • @balasankarajith2923
    @balasankarajith2923 4 года назад +4

    Me at the begining of the video - Ah this gonna be easy, just a short simple steps.
    The steps - *John Cena's voice* : Are you sure about that?

  • @angelbunny225
    @angelbunny225 9 лет назад +4

    Wow thank you so much! You saved my life in this crappy maths class.

  • @Kaamz1926
    @Kaamz1926 4 года назад +14

    2:28 he says we need to subtract red numbers from the green numbers and then he does exactly the opposite

    • @southernkatrina8161
      @southernkatrina8161 4 года назад +2

      Yep -5. I think he just said it wrong.

    • @cankarayel5063
      @cankarayel5063 3 года назад

      Determinant is 5. He did it true but he said that wrong.

  • @oderajohana
    @oderajohana 10 лет назад

    This the best explanation of all the videos for finding inverse. thanks very much

  • @TimerUchiha
    @TimerUchiha 10 лет назад +24

    It's so stupidly long and tedious, nonetheless great vid

  • @CaityRaindrop
    @CaityRaindrop 10 лет назад

    I found this very helpful, trying to self teach myself this material for a transfer exam to change courses and the book just jumped straight into asking questions without even giving a formula.

  • @AsraHussain
    @AsraHussain 9 лет назад +3

    Thank you sooooooooooooooo much this helped me alot...god bless yuh!

  • @SuzyW3323
    @SuzyW3323 5 лет назад

    dude. a literal lifesaver. 10/10

  • @GreaterDeity
    @GreaterDeity 9 лет назад +52

    This method made absolutely no sense to me; seems very arbitrary, but it's right.

    • @GreaterDeity
      @GreaterDeity 9 лет назад

      ***** Ill just admit I am too stupid for this one. I tried going over it for a good 30 minutes and couldnt find the logic of the pattern.

    • @GreaterDeity
      @GreaterDeity 9 лет назад

      I do the same to find the inverse, but it gets really confusing if I use the determinant. Row ops and Gaussian Elimin. aren't that bad, as long as I don't make arithmetic errors.

  • @vishvapatel9544
    @vishvapatel9544 4 года назад

    I have remote learning right now because of Coronavirus and we’re learning matrices and this video helped a LOT.

  • @kree5423
    @kree5423 5 лет назад +4

    i had to try and fit this whole video into 1/6 of my reference sheet

  • @parasharpanchal6857
    @parasharpanchal6857 8 лет назад +1

    man... the way u calculated the determinant was amazing ... thank u sooooo much .. i had already studied matrices in my previous semester but i had to recall it and i referred to ur video and it blew my mind.... keep on making such videos with ur own techniques.. thanks a lot buddy

  • @rasberry272
    @rasberry272 8 лет назад +52

    This method seems super impractical

  • @bryce7355
    @bryce7355 7 лет назад +1

    Perfect. I needed a brief review. Engineering courses use linear algebra and all the good stuff with variables, so it usually is a little more pencil being pushed down. And tears, don't forget the tears...

  • @Shane8
    @Shane8 10 лет назад +6

    That is the arbitrary process I have ever seen.

  • @omermirza3210
    @omermirza3210 5 лет назад

    One of the most well explained tutorial over youtube

  • @konnichiwa8762
    @konnichiwa8762 10 лет назад +5

    Thank you very much!! This video already help me a lot with my assignment ^_^

  • @ansau5556
    @ansau5556 11 лет назад

    many many many thanks!!!! you saved my Calculus test from being the worst test that I've ever had!
    Keep moving on!!!
    with love! :)))))

  • @orealz
    @orealz 6 лет назад +6

    What if the determinant turns out to be a negative number?

    • @berkburakbiyikli5655
      @berkburakbiyikli5655 5 лет назад

      It will still be alright. The negativity could only show the direction so as along as the determinant is not zero, it will have an inverse.

  • @felipemadalengoitia9292
    @felipemadalengoitia9292 2 года назад

    this appeared in my recommended and now I know how to inverse a 3x3 matrix. Thank you

  • @عبدالرحمنالسنوسى-ص9س

    شكرا جدا انا مكنتش فاهم اجيب مرافقات المصفوفه ازاى دلوقتى بقيت اعرف و لو جت فى الامتحان مش حامل همها

  • @mikesmate6672
    @mikesmate6672 6 лет назад +1

    Thanks bro I love these steps they are fast and straight to the point, sure the computer gives the answer instantly because all these steps were incorporated into it by someone who knew them.

  • @rimberse3405
    @rimberse3405 4 года назад +10

    14:38 ahah, nice ending lmao
    Nearly destroyed my self-esteem...
    I would probably spend over 40min...

  • @nziom
    @nziom 5 лет назад +1

    Finally a RUclips video worth of 1+ million viewers

  • @Xmasparol
    @Xmasparol 10 лет назад +61

    who invented this?

    • @retroSTAAR
      @retroSTAAR 10 лет назад +23

      looool im thinking the same thing i mean what is the point

    • @RenzoIsHereYT
      @RenzoIsHereYT 6 лет назад +2

      James Bondoc in CP matices work so different

    • @jonbowman7686
      @jonbowman7686 6 лет назад +26

      In engineering, we actually use this to solve multiple dynamics equations simultaneously, so we can determine how all the different parts of a mechanism will move- like all the positions and max/min angles of all the parts in an engine for example. I had to refresh my memory of how to do this lol, that's what brought me here.

    • @glittergirl19022
      @glittergirl19022 6 лет назад

      exactly. i mean why

    • @thewarlord6529
      @thewarlord6529 6 лет назад +7

      A random genius 200 years ago, that never even thought about how much misery he was inadverdently causing among future high school students.

  • @sulangnelson7269
    @sulangnelson7269 6 лет назад

    finally..took a month for me searching for this type of video..very helpful...perfect

  • @XrGrimreap3rX
    @XrGrimreap3rX 9 лет назад +8

    What if the determinant is 0?

    • @redadrissi4460
      @redadrissi4460 6 лет назад +1

      you will have to pseudo inverse it

    • @ttvurmom6185
      @ttvurmom6185 6 лет назад

      Then you quit math class and start gambling.

  • @Rayquesto
    @Rayquesto 11 лет назад

    It's easier than it looks. All he did was: 1) find the determinant, 2) calculate minors (or a bunch of individual 2 by 2 determinants) corresponding to the junction of the crossed out row and column to that single entry (a junction is a point where those two lines you'd use to cross either rows or columns meet), 3) transpose that matrix, 4) divide every number in that matrix by the determinant of the matrix you want to take the inverse of.

  • @GermanSnipe14
    @GermanSnipe14 10 лет назад +39

    Lol if people are learning matrices, I'm pretty sure they know arithmetic, you don't need to waste time explaining how to subtract numbers

    • @weeeho8005
      @weeeho8005 6 лет назад +14

      Lol if people are learning matrices on youtube, I'm pretty sure they know they can skip parts of the video, you don't need to waste time explaining how to explain better

    • @myhops
      @myhops 6 лет назад +6

      I think it is necessary, because with your mindset, it's easy to assume too much and leave out parts that can be easily forgotten or overlooked.

    • @crwelch12
      @crwelch12 6 лет назад +6

      you clearly underestimate the human race's ability to fuck up

  • @shantanu925
    @shantanu925 6 лет назад +1

    World needs more guys like you!

  • @AK.
    @AK. 11 лет назад +3

    what if this was a 4x4 matrix? Would I have to draw 4 diagonal lines?

    • @iohanb211
      @iohanb211 11 лет назад

      no,it does not work this way,it is a special way on 4x4 but i cant remebrer:(

    • @1ThomasTom
      @1ThomasTom 10 лет назад +3

      Iohan Kellerman You'll have to write a 4x4 matrix of which all diagonal entries from left above to right under are 1 and the non-diagonal 0. Place this matrix next to the 4x4 you want to know the inverse of. Then row reduce this new 4x8 matrix so that the left 4 columns look like the matrix you wrote next to your original matrix (with the 1's and 0's). If you've done this correctly, you'll see the inverse of your matrix in the right 4 columns of the 4x8 matrix. I think this works for every matrix that is invertible. You can try it out on the 3x3 in this clip to see if you understand.

    • @iohanb211
      @iohanb211 10 лет назад

      I see,but i don't need 4X4 matrix,my exams are how can i say a medium difficulty,i just needed to remember how it works on a 3x3!Thank you!

  • @adafulajwayirechristopher272
    @adafulajwayirechristopher272 8 лет назад

    I just give thumps up to this teacher. Thanks for uploading this video.

  • @bh4t128
    @bh4t128 10 лет назад +3

    hard way to solve inverse of 3x3 matrix

  • @CrownedBasiliskDX
    @CrownedBasiliskDX 8 лет назад

    Very comprehensive and easygoing guide, you are a god!

  • @billtruttschel
    @billtruttschel 10 лет назад +11

    I'm really annoyed by a few things in this video. First, at 2:25, you said you were going to subtract the red numbers from the green numbers, when you clearly did it the other way around. Second, at roughly 12:00, you have two different matrices that you're calling N. Third, N itself is a matrix, so when you write [N] you are saying the matrix consisting of the matrix N, which is also wrong.

    • @ttvurmom6185
      @ttvurmom6185 6 лет назад

      Bill T I caught that too, bro.

  • @brunosanchez6294
    @brunosanchez6294 6 лет назад

    Love how you go slow step by step even on the super simple multiplications 👏🏻

  • @rajaninair4377
    @rajaninair4377 8 лет назад

    thank u so much.....i was very confused to do the inverse of matrix before watching this video. you explained it in an efficient way any body can understand easily. Excellent !!!!!

  • @corpliner1506
    @corpliner1506 6 лет назад +2

    Thank you for a concrete method of finding inverse. I can follow the exact same process each time unlike row operations

  • @ripfumelohlungwani2812
    @ripfumelohlungwani2812 7 лет назад +1

    thank you bro, you've just simplified this nightmare to me. it was giving me a tough time until i come across this video.

  • @rodericksibelius8472
    @rodericksibelius8472 3 года назад

    I have never learned this while I was studying my 2 Year degree in Electrical/Electronics Engineering Technology, the electronic math instructor just taught us the CRAMERS Rule for Solving 3 unknowns. I had no IDEA of a MATRIX INVERSE and WHY or Where it is used for. I like the detail the procedure step by step How this INVERSE MATRIX can be done. Now I think I'm going to 'write a Computer program' as an exercise in Python... just have something to do as a RETIRED engineering technician... LOL!!!!...

  • @rojecanby23
    @rojecanby23 11 лет назад

    Marcellin Mutuyimana has got the right idea. Using Gaussian elimination and putting an identity matrix next to your original matrix will yield the inverse.

  • @Alroqi5111
    @Alroqi5111 2 года назад +1

    جميل جدًا وفي غايةِ الوضوح ، شُكرًا لك .

  • @theboringdev
    @theboringdev 8 лет назад

    you are way more better than my lecturer!!!! Good Job Dude!!!!

  • @I_aint_no_groot
    @I_aint_no_groot 9 лет назад

    you don't know to what extent you've helped me with your video ;-))) that was so awesome. what I couldn't keep in my mind for more than 3 years, easily stuck in my mind .
    thanks so much for your great video

  • @HDitzzDH
    @HDitzzDH 5 лет назад

    10:48 I think it's easier to just say that the rows becomes the columns (first row becomes the first column, second row becomes the second column etc), perhaps it makes it easier to grasp what we're doing (at least it was for me).

  • @carmenwong9711
    @carmenwong9711 8 лет назад

    you taught really well and i love your last sentence

  • @jayn5543
    @jayn5543 2 года назад

    im certain i learned all of this in my class, but i was barely awake and only retained like half of this, so thanks for saving me

  • @SundaresanMuthuswamy
    @SundaresanMuthuswamy 3 года назад

    VERY NICELY DONE. Thank you for the clarity and approach.

  • @hichamouazi
    @hichamouazi 10 лет назад +3


    Thank you, this is the easiest way to inverse a matrice so far I guess

  • @Don_Cute-xote
    @Don_Cute-xote 3 года назад +1

    This is so much easier than doing row operations... BIG THANKS!!! I managed to do my assignment thanks to this :D

    • @theboldguy.
      @theboldguy. 2 года назад

      On row operations you may stuck like crazy and always go from 0's on the diagonial to positive numbers back and forth never getting a solution .....

  • @kayouel4551
    @kayouel4551 8 лет назад

    i have an exam tomorrow and u just helped me thank u so much, from morocco

  • @siddharthbanerjee2816
    @siddharthbanerjee2816 4 года назад

    the unique style of calculating Determinant won the day

  • @guilhermealves9795
    @guilhermealves9795 5 лет назад

    Congratulations, you have a lot of patient and are an excellent teacher!

  • @nirtime
    @nirtime 8 лет назад

    Thank you so much, I am at university level and this should be something extremely basic but the instruction suck! This here just made it easy.

  • @lynnnevins9089
    @lynnnevins9089 2 года назад

    Thank you soooo much. I was searching how to do it for 8 hours.

  • @deemaalatawy1025
    @deemaalatawy1025 3 года назад

    Oh thank you very much. This is the first time I've commented on someone
    , but you understood me so well 👍👍

  • @TheLasituation
    @TheLasituation 7 лет назад

    Big thanks from Belgium!

  • @jasmeenrahman3298
    @jasmeenrahman3298 11 лет назад

    thank you! you have been of great help for my last minute assignment submission! :)

  • @khaddyceesaydaffeh6188
    @khaddyceesaydaffeh6188 3 года назад

    This video is really a life saving one....thanks so much Sir. God bless you

  • @postholedigger8726
    @postholedigger8726 7 лет назад

    Baldy Hardnut,
    The secret to learning this is: PRACTICE, PRACTICE, PRACTICE, PRACTICE ,PRACTICE.......+ PRACTICE. The reason math teachers are so good at this stuff is because they do it day after day, year after year. Some people may seem to grasp it sooner than others but at some point, for almost everybody, it becomes part of your thought process. Once a person learns that 2 + 3 = 5, having a PhD in mathematics does not produce a different result.
    david

  • @sebastianringlstetter6103
    @sebastianringlstetter6103 6 лет назад +1

    Bless your soul, you beautiful man. I have no idea how you made this up, but it works like a dream. Thank you so much

  • @pesoretrl3447
    @pesoretrl3447 6 лет назад

    Dozens of thanks and thanks in all language ...u r just awesome. ...thanks brother, teacher, sir ☺☺☺☺☺☺

  • @theguyaneseumbrella2762
    @theguyaneseumbrella2762 5 лет назад +1

    Its 2019 and this still helped me ... thank you

  • @MrJames11311
    @MrJames11311 11 лет назад

    Thank you so very much. I'm only a sophomore in my Alg.II class full of juniors and they still haven't gotten the concept. I think this video should help them.

  • @riturajawat4312
    @riturajawat4312 4 года назад +1

    Thank you so much sir for this video

  • @muleyaluyando7889
    @muleyaluyando7889 3 года назад

    Thank you very much....finally I get it after so long 😭😭😭😭❤️❤️❤️❤️❤️❤️❤️❤️❤️ you saved my exam

  • @hienle1153
    @hienle1153 6 лет назад

    Very clear explanation. Wish my teacher have made it clear like you. Thank you so much.

  • @danielle_le
    @danielle_le 3 года назад +1

    This was a thorough and well-paced explanation. Thank you so much and keep up the great work.

  • @Duckington10
    @Duckington10 8 лет назад

    The part about reflecting the elements in the diagonal line is the transpose of the matrix which is where rows become columns and columns become rows.

  • @topsixgaming
    @topsixgaming 3 года назад

    Thanks man. You’re genius! 🙌🏽 this is so comprehensive! 😭😭🙌🏽🙌🏽

  • @spmcdade901
    @spmcdade901 6 лет назад

    Thanks, that was very easy to follow. Much better than drawing loads of random triangles

  • @كيانريماس-ح1ض
    @كيانريماس-ح1ض 8 лет назад

    thank you realy ،شكرا فهمت وربي احس من المس اللي عندي :)♡