Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 1

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  • Опубліковано 1 сер 2010
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    Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 1. Besides using row reduction, this is another way to find the inverse of a 3 x 3 matrix.

КОМЕНТАРІ • 785

  • @theshouter3285
    @theshouter3285 7 місяців тому +162

    Anyone in 2024?❤

  • @Howsonify
    @Howsonify 10 років тому +627

    For those who want a simpler method for 5:10 and on (without "reflecting things about the diagonal"): Just *transpose* the matrix, which means the first row becomes the first column. The second row become the second column. The third row becomes the third column. The nth row becomes the nth column. It's easier to remember this way.

    • @anuprandive5145
      @anuprandive5145 6 років тому +8

      Thanks

    • @ssss855167
      @ssss855167 4 роки тому +4

      Thank you.

    • @dremr2038
      @dremr2038 4 роки тому +4

      That is adjoint, right?

    • @osmanmehmood3580
      @osmanmehmood3580 4 роки тому +18

      @@dremr2038 Yes, finding the cofactor of each element of the matrix and transposing it, gives us the adjoint of the matrix in question. Dividing that by the determinant of the original matrix gives us the inverse of the matrix.

    • @ZikreMustafaSAW
      @ZikreMustafaSAW 4 роки тому +1

      Ok

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    @patrickjmt  13 років тому

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    @vikkalkat2241 10 років тому +183

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  • @chillindylan1786
    @chillindylan1786 9 років тому +773

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  • @SuperFerdie1965
    @SuperFerdie1965 5 років тому +61

    I've been a maths tutor for 42 years and I haven't the faintest idea why this works! Thanks for a very good demo.

    • @karanbharadva9820
      @karanbharadva9820 2 роки тому +8

      Wasted 42 years

    • @SuperFerdie1965
      @SuperFerdie1965 2 роки тому +19

      @@karanbharadva9820 I wouldn't say that a millionaire tutor has wasted his time tutoring!!

    • @karanbharadva9820
      @karanbharadva9820 2 роки тому

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      @SuperFerdie1965 2 роки тому +1

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      @metaverse413 8 місяців тому +1

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  • @isabellatieu8404
    @isabellatieu8404 9 років тому +3

    I've already thanked you on another video, but I just can't thank you enough! My prof spent 1.5 hours on each matrix topic. None of it made sense and some people even got up to leave in the middle of lecture. Thank you for making everything 100% clear.

  • @chriswilliams5291
    @chriswilliams5291 2 роки тому +5

    I've watched quite a few videos on finding the inverse of a 3 x 3 matrix and so far your method seems like the easiest way to do it without making mistakes. Thanks for sharing!

  • @canadianthroneholder
    @canadianthroneholder 10 років тому +165

    Why do these formulas work, who came up with this method for finding the inverse of a 3x3 matrix and what was going through his head at the time?

    • @thabi.b7128
      @thabi.b7128 9 років тому +11

      I Know what you mean like gezz.. some guy comes up with a method then others find a better way to do what you came up with... like WTF... its so Heavy..

    • @canadianthroneholder
      @canadianthroneholder 9 років тому +8

      Mthabisi Bokete with linear algebra in general i see a lot of fancy tricks and algorithms for solving problems but never a proof showing why they work

    • @kdu8004
      @kdu8004 9 років тому +8

      Marcus Fenix Aliens.

    • @derekroolz
      @derekroolz 9 років тому +7

      Marcus Fenix You don't want to see the proofs lol. Well, some are easy and some are harder, some are very trivial, but extraordinarily long. Determinants revolves a lot around matrix multiplication. Matrix multiplication's proof isn't too bad if you remember your matrix as a set of vectors in the defined r-space.

    • @canadianthroneholder
      @canadianthroneholder 9 років тому +3

      derekroolz I saw some wikepedia proof for the cofactor expansion and didn't understand it at all

  • @sangeetharamamurthy8628
    @sangeetharamamurthy8628 8 років тому +20

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  • @yungfillly
    @yungfillly 10 років тому +268

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    @iki0o 10 років тому +123

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    @lifewithdylan 6 років тому +208

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    @syd_jzx100 8 років тому +3

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    @benitocarlos0 3 роки тому +5

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    @davidontiveroz8295 7 років тому +1

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  • @kemarbeckford8281
    @kemarbeckford8281 9 років тому +1

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  • @pd7009
    @pd7009 7 років тому +1

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    @asnsr3573 8 років тому

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  • @MrCtown8
    @MrCtown8 10 років тому +19

    My professor barely speaks English, these videos are so useful! thanks

  • @rajendramisir3530
    @rajendramisir3530 2 роки тому

    Good work Patrick. Identifying the matrix of minors, matrix of cofactors and the adjoint matrix will help viewers follow and understand the various steps in arriving at the inverse matrix of the original 3 by 3 matrix.

  • @Luna-fu7ix
    @Luna-fu7ix 6 років тому +1

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    @cleomanloloyo1950 8 років тому +1

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    @Zaratron-rd1jk 9 років тому +8

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    • @patrickjmt
      @patrickjmt  9 років тому +7

      Glad you like my videos!

    • @Zaratron-rd1jk
      @Zaratron-rd1jk 9 років тому +3

      I did indeed! I finally used it today and aced it! xD Thanks so much again for taking the time to help others! (:

  • @rpf19
    @rpf19 12 років тому +1

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  • @jingyiwang5113
    @jingyiwang5113 Рік тому +1

    I am really grateful for this explanation! This is definitely very helpful! Thank you so much!

  • @prabhakarramachandran9784
    @prabhakarramachandran9784 5 років тому +1

    This could never get even more clear to me. Thank you soo much

  • @patrixemary2187
    @patrixemary2187 3 роки тому +2

    i've been trying to understand this lesson which was never discussed by our prof and u just saved lives :(( thank u

  • @RebeliousSapien
    @RebeliousSapien 5 років тому

    this was thorough and very well explained.
    thank you so much for the help

  • @systempatcher
    @systempatcher 6 років тому +134

    You confused me with the whole diagonalization thing. Took me a second to realize it's just a transpose lol...

  • @lovelaughdance98
    @lovelaughdance98 9 років тому

    Your videos are helping me sooo much! gonna ace this midterm thanks to you :)

  • @sayem.wayeez
    @sayem.wayeez Рік тому +1

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  • @patrickjmt
    @patrickjmt  12 років тому

    @haybaby95 my pleasure, glad i could help : )

  • @abdullahisaahmed5366
    @abdullahisaahmed5366 10 років тому +4

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    @saminchowdhury7995 7 років тому

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    @share-up3503 8 років тому

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  • @avonbarksdale418
    @avonbarksdale418 5 років тому +7

    5:25, It can also be referred to finding the transpose or adjoint of the matrix. The rows become columns, and the columns become the rows. Good job.

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    @Khaielaash94 12 років тому +4

    You don't know how much you're helping me in A Level Further Math. :D
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  • @TOFFY-kd7pe
    @TOFFY-kd7pe 4 роки тому +8

    What my teacher says :
    "It's simple :" *Complicated, incomprehensible stuff on the board wich he erases every seconds*
    Him :
    *Explains ORALLY an actual simple method in addition of explicitly witting it down AND doing it on UA-cam, giving us the ability to pause or rewind.*

  • @friedbabyfingers
    @friedbabyfingers 10 років тому +16

    Why can't teachers be this straight forward?

  • @Crime-Politics
    @Crime-Politics 3 роки тому

    Thank you so much for the videos! I was running late on recapping and this video (hopefully) made the difference.

  • @mohitshirpurkar9455
    @mohitshirpurkar9455 4 роки тому

    Thanks for making the video I understood it within 1 minutes and now I can solve every inverse questions in 3-5 minutes.

  • @AmanKumar-te8ft
    @AmanKumar-te8ft 4 роки тому

    This is the method for which I was looking for about an hour.
    Thanks🙏🙇

  • @nikhilkoirala8633
    @nikhilkoirala8633 5 років тому +3

    Thank you so much. It really helped me alot

  • @suvasish.dey.sarker.bangladesh
    @suvasish.dey.sarker.bangladesh 7 років тому

    I have a midterm tomorrow, thanks a ton brother!
    I'm hopefully gonna ace it tomorrow thanks to you!
    Love from Bangladesh!

  • @dewpiedie5348
    @dewpiedie5348 6 років тому

    Thank you so much! That was such an awesome explanation!

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    @JustinRoy-hv7bt Місяць тому

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  • @ibrahimmaqdam6020
    @ibrahimmaqdam6020 8 років тому +1

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    Thanks alot Bro

  • @Aldosary0543
    @Aldosary0543 12 років тому

    Your videos helped me understand math a lot better than classes! Thanks man

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    @jamiewu5618 9 років тому +44

    Holy mother of god, my brain is fried.

    • @Mr-WesleySnipzzz
      @Mr-WesleySnipzzz 6 років тому +2

      My brain exploded

    • @Peter-bg1ku
      @Peter-bg1ku 3 роки тому

      In my opinion, the only difficult part of this tedious process is avoiding making small mistakes. The concept itself is fairly easy to grasp.

  • @katherinedeoliveira8777
    @katherinedeoliveira8777 6 років тому +1

    This helped me so much! Thank you!!

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    @patrickjmt  12 років тому +6

    @gudefeda i freakin' love the internet. i am old enough to remember when our school got our first computer in 4th grade, when the family got an atari 2600, when i got my first computer at home ( run dos, run), dial up modems that took 10 hours to load a picture, and finally, a good internet connection. god bless al gore for inventing the internet

  • @kevinshi270
    @kevinshi270 6 років тому

    Super good video, clear and easy to understand!!

  • @frozenporcupine
    @frozenporcupine 3 роки тому

    Really easy to understand! Thank you so much!!!

  • @sandeepkashetty455
    @sandeepkashetty455 7 років тому +1

    awesome sir.very interesting,thanks for teaching the 3*3 matrix very easily

  • @sabaharefin4852
    @sabaharefin4852 9 років тому

    this is so much better than reading the book and reading the examples which doesn't make much sense most of the time... thank you for making it easy.

  • @davida6386
    @davida6386 7 років тому

    wow makes a lot more sense now. thank you. Tedious work but doable

  • @googleuser4577
    @googleuser4577 5 років тому +2

    YOUR WRITING IS AMAZING

  • @junaidahmad3622
    @junaidahmad3622 8 років тому

    it was mind blowing solution thanks bro
    KEEP doing good work
    it seems like it easy to handle such the kind of problems
    thanks again

  • @GladanDsouza
    @GladanDsouza 3 роки тому

    Your a legend dude. YOU SAVED ME WEEKS!

  • @khaled_ismail
    @khaled_ismail 9 років тому

    Thanks man. Nice explanation, short time.. Awesome job :)

  • @leohnherschel3836
    @leohnherschel3836 5 років тому +2

    you just saved me.thank you.
    had problem with that.thanks buddy

  • @rampatel4817
    @rampatel4817 4 роки тому +1

    I’m watching this dude 9 years later and he saved me thanks

  • @isabelncube7584
    @isabelncube7584 3 роки тому

    thank you so much your information was really helpful now l fully understand the concept

  • @JuanYe_West
    @JuanYe_West 12 років тому

    Definitely more helpful that my math teacher! Thanks a bunch!

  • @patrickjmt
    @patrickjmt  12 років тому

    @no2475 unfortunately, that is how many math classes are structured in usa. when i taught, we had to go fast as we had to cover waaaaaaay to much stuff typically; if we fell behind, we got in trouble at the end of the year. no good for anyone.

  • @Ceejaymovies
    @Ceejaymovies 2 роки тому

    thank u very much i didn`t understand sign when doing cofactors but now i do u the best

  • @amerdhiab
    @amerdhiab 8 років тому

    Thank you sir for all the videos!!!

  • @kimiko495
    @kimiko495 7 місяців тому

    wow this is really complex, but you explained well and I understood the procedures, thanks a lot!

  • @parvgoyal6324
    @parvgoyal6324 8 років тому

    thanks mate upload more videos regarding integration and differentiation and compound interest and annuity from the basic.
    You have a got a very good teaching skills.

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    @emandleni1735 8 років тому +25

    You're a legend!

    • @patrickjmt
      @patrickjmt  8 років тому +3

      Thanks! :)

    • @fredijacksi9801
      @fredijacksi9801 7 років тому

      patrickJMT I'm going to take my entrance exam for M.A Economic..so would you mind calculating some of my doubt questions for me ? plss...I will be grateful if you do so..pls leave me your email address here or any social network where I can post my questions series. thank you!

  • @redsoldier568
    @redsoldier568 7 місяців тому

    Thank you. Watching this 1 hour before my exam, learned something new

  • @varungoyal4732
    @varungoyal4732 4 роки тому

    THANK YOU SO MUCH PATRICK! YOU JUST SAVED MY LIFE.

  • @williamyuhanhou5170
    @williamyuhanhou5170 4 роки тому

    finding an inverse is a truly painful process, but u did it in a way that made me understand it.

  • @JasonChamberlain
    @JasonChamberlain 11 років тому

    dude. you are one of the most helpful people out there.

  • @liamchandler8860
    @liamchandler8860 8 років тому +3

    Easy, quick. Thanks

  • @FURYofCURRIE
    @FURYofCURRIE 10 років тому

    you just explained this way better than my prof and TA could. Thank you

  • @Pinky-ei7ub
    @Pinky-ei7ub 2 роки тому

    Wow. Thank you so much. I actually prefer this method over Gauss Jordan for inverses because Gauss Jordan for me is tideous and mistakes are easily made so with this one, it is easy to keep track of your workings.

  • @DatLewdogTho
    @DatLewdogTho 9 років тому

    Brilliant, simple and informative :)

  • @brayancarrera9787
    @brayancarrera9787 10 років тому

    Thank you for this! This really helps!

  • @PyroPioneer
    @PyroPioneer 4 місяці тому

    13 years later and you're still helping people with this video ❤ thank you

  • @faithfelix7816
    @faithfelix7816 9 років тому

    thank you much
    you help me a lot to understand it well

  • @hassanalmahdi8358
    @hassanalmahdi8358 8 років тому

    Thanks for always helping me man , cheers

  • @wanni_zr842
    @wanni_zr842 5 років тому

    my lecturer showed me the rref way, just found this is more useful and spend less time. Thank you!!!!

  • @digvijaysinhparmar6439
    @digvijaysinhparmar6439 5 років тому

    Thanks sir it really helped me understanding the concept

  • @sabrinaalgoo1822
    @sabrinaalgoo1822 9 років тому +1

    you're the best teacher on youtube to my knowledge thank you :DDDDDDDDDDDDD

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    @fakihababar 2 роки тому

    I have an exam in about 3 hours and you just saved my life thank you soooo muchh

  • @emrglr6963
    @emrglr6963 3 місяці тому

    your videos still work like magic in 2024. I passed my calculus courses thanks to your videos 10-11 years ago.

    • @patrickjmt
      @patrickjmt  3 місяці тому

      glad i could still help :)

  • @minttea9140
    @minttea9140 2 роки тому

    I know this is an 11 year old video, but sir, wherever you are now, bless you!!! I had a breakdown after my first math class because the professor did not explain this well at all, but just after watching this video I understand it all :D

  • @shanielching6868
    @shanielching6868 Рік тому

    Trust me I found it hard to find a strategy for finding co factors ..... And u jxt made it look so easy thank u

  • @gafourfaiza2525
    @gafourfaiza2525 8 років тому

    thank u so much it was so helpful and easy to understand ( i study in frensh and am not very good in english ) good Luck 😊

  • @ahamadromen
    @ahamadromen 7 років тому

    Thank you , very nice work, helpful !!!

  • @Sandeepyadav-sp4sm
    @Sandeepyadav-sp4sm 4 роки тому

    Thankyou for the video it was really helpful

  • @daltonfelt0828
    @daltonfelt0828 5 років тому

    Thank you very much. Very clear guide.

  • @Aoskar95
    @Aoskar95 9 років тому +48

    Way sampler than gauss elimination. Why doesn't my math teacher teach this.

    • @rudyeilabouni
      @rudyeilabouni 7 років тому +6

      Actually for simpler matrix entries, I think the Gauß elimination is much faster... Sometimes you can find the inverses with a handful of steps... This seems to be for tougher matrices... It's good to know both I guess.

    • @RubaiVideos
      @RubaiVideos 6 років тому

      Gaussian elimination has fewer steps to find the inverse. The determinant is computationally inefficient

    • @atchutram9894
      @atchutram9894 6 років тому

      Gaussian works for any order of the matrix.

  • @haniabdullahi2095
    @haniabdullahi2095 7 років тому

    THANK YOU SO MUCH FOR MAKING MATH EASY.. I TRULY APPRECIATE

  • @chavanomkar8276
    @chavanomkar8276 6 років тому

    Thank you so much I just got understand how to do it

  • @fatimasaleh4721
    @fatimasaleh4721 4 роки тому

    You made it very easy, thank you