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

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  • Опубліковано 8 січ 2025

КОМЕНТАРІ • 807

  • @Howsonify
    @Howsonify 10 років тому +658

    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 7 років тому +8

      Thanks

    • @ssss855167
      @ssss855167 5 років тому +4

      Thank you.

    • @dremr2038
      @dremr2038 5 років тому +4

      That is adjoint, right?

    • @osmanmehmood3580
      @osmanmehmood3580 4 роки тому +19

      @@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.

    • @JamateSirajiaFaisalabad
      @JamateSirajiaFaisalabad 4 роки тому +1

      Ok

  • @vikkalkat2241
    @vikkalkat2241 10 років тому +192

    thank you so much! after i graduate and work full time, my first paycheck will be sent to you

  • @SuperFerdie1965
    @SuperFerdie1965 6 років тому +64

    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 +9

      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

      @@SuperFerdie1965 haha lol 😁

    • @SuperFerdie1965
      @SuperFerdie1965 2 роки тому +1

      @@karanbharadva9820
      Not all are losers and morons like yourself my poor little troll!

    • @metaverse413
      @metaverse413 Рік тому +1

      @@SuperFerdie1965 sounds like a 9 years old to me

  • @chriswilliams5291
    @chriswilliams5291 2 роки тому +7

    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!

  • @theshouter3285
    @theshouter3285 Рік тому +218

    Anyone in 2024?❤

  • @sangeetharamamurthy8628
    @sangeetharamamurthy8628 9 років тому +21

    This video literally saved me from failing my midterm! You're incredible!!!!

  • @crunchiecat
    @crunchiecat 11 років тому +268

    every lecturer/teacher should just show this in class rather than saying a word out their mouth

  • @cleomanloloyo1950
    @cleomanloloyo1950 8 років тому +3

    different generations are going to watch this video of yours over and over again :-) thank you so much patrick :-)

  • @canadianthroneholder
    @canadianthroneholder 10 років тому +169

    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 10 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 10 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 10 років тому +8

      Marcus Fenix Aliens.

    • @derekroolz
      @derekroolz 10 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 10 років тому +3

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

  • @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.

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    @syd_jzx100 8 років тому +3

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    @iki0o 11 років тому +124

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    @jarlhamm 6 років тому +1

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    @MrCtown8 11 років тому +19

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    @rpf19 12 років тому +1

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    @Zaratron-rd1jk 9 років тому +8

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    • @patrickjmt
      @patrickjmt  9 років тому +7

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      @Zaratron-rd1jk 9 років тому +3

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    @googleuser4577 5 років тому +3

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  • @avonbarksdale418
    @avonbarksdale418 6 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.

    • @its_houssem
      @its_houssem 7 місяців тому

      Yeah this is the trick !

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    @lifewithdylan 7 років тому +208

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      @wentworthmiller1890 6 років тому +6

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      @pluto40433 6 років тому

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      @NMQ098 6 років тому

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      @andreaelan7267 5 років тому

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  • @davidontiveroz8295
    @davidontiveroz8295 7 років тому +1

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  • @karim4388
    @karim4388 6 місяців тому +1

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    • @patrickjmt
      @patrickjmt  3 місяці тому

      thanks! glad that i could help you after all this time :)

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    @patrixemary2187 4 роки тому +2

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    @jinxIomI 10 місяців тому

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    @Judyangieli 11 років тому

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  • @TOFFY-kd7pe
    @TOFFY-kd7pe 5 років тому +8

    What my teacher says :
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    @sabaharefin4852 10 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.

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    @sayem.wayeez 2 роки тому +1

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  • @marrinnalee2978
    @marrinnalee2978 3 дні тому

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    @friedbabyfingers 11 років тому +16

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    @doggy4721 Рік тому

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

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    @legendsplayground7017 2 місяці тому

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    @shookycooky5498 2 роки тому

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    @JustinRoy-hv7bt 7 місяців тому

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    @minttea9140 3 роки тому

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    @emrglr6963 8 місяців тому

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    • @patrickjmt
      @patrickjmt  8 місяців тому

      glad i could still help :)

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    @GLDN06 3 роки тому

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    @emandleni1735 8 років тому +25

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    • @patrickjmt
      @patrickjmt  8 років тому +3

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      @fredijacksi9801 7 років тому

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    @ibrahija 11 років тому

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    @JasonChamberlain 12 років тому

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    @Khaielaash94 12 років тому +4

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    @fakihababar 2 роки тому

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  • @no2475
    @no2475 13 років тому

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    I learned more from your videos than I did from her.

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    @patrickmorel1809 12 років тому

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    @mumbakondowe6839 3 роки тому

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    @manojkumarsubramaniam7122 7 років тому

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    @ronaldkisitu8401 4 роки тому

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    @alfredmerin5445 2 роки тому

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  • @williamyuhanhou5170
    @williamyuhanhou5170 5 років тому

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

  • @systempatcher
    @systempatcher 7 років тому +135

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

  • @dan-bf5ie
    @dan-bf5ie 2 роки тому

    thank you, this is saving me 2 hrs before my exam

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    @craigdow5566 12 років тому

    Man thanks to your video's I may actually pass my exam tomorrow. Cheers!

  • @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!

  • @Sai-pi4wq
    @Sai-pi4wq 10 місяців тому

    AHHHH I remember my teacher doing this method in the class but I forgot it. Thank you so much!! Hope I can use this is my exam tomorrow.

  • @varungoyal4732
    @varungoyal4732 5 років тому

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  • @85mopao
    @85mopao 12 років тому

    man you just saved me thanks for the time that you had spend on this saving video

  • @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.

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    @tayyab.sheikh Рік тому

    I'm in love with your handwriting.

  • @burningburgerx4023
    @burningburgerx4023 3 роки тому

    much simpler and easier than school
    thanks for the help!!

  • @benitocarlos0
    @benitocarlos0 4 роки тому +5

    Long time no see you, my friend. Just doing a semester in modern controls in EE and I am studying for the final that will probably have this. Thanks for your work.

  • @prabhakarramachandran9784
    @prabhakarramachandran9784 6 років тому +1

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

  • @bullterry14
    @bullterry14 9 років тому

    thumbs up if this guy is like your second and most useful teacher

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    @chhavishyamtiwati6524 2 роки тому

    Best style for teaching

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    @sabrinaalgoo1822 9 років тому +1

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  • @msucds1
    @msucds1 12 років тому +3

    Thank you so much!!! My teacher tries to make this so hard by using the row reduction echelon form. Now thanks to you I am going to show him!

  • @jamiewu5618
    @jamiewu5618 10 років тому +44

    Holy mother of god, my brain is fried.

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      @Mr-WesleySnipzzz 7 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.

  • @khanhcamhoang2118
    @khanhcamhoang2118 2 роки тому +1

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    @nikhilkoirala8633 5 років тому +3

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  • @kimiko495
    @kimiko495 Рік тому

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

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    @shubhambhardwaj4428 6 років тому

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  • @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!!!!

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    @erfanchowdhury9837 10 років тому

    You just earned yourself a fan!

    • @patrickjmt
      @patrickjmt  10 років тому +5

      great! glad you like the videos

  • @sandeepkashetty455
    @sandeepkashetty455 7 років тому +1

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

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    @박서준-b6d1k 3 роки тому

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    @asnsr3573 9 років тому

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    @saminchowdhury7995 7 років тому

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    @gudefeda 13 років тому

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    @squishymushy0037 3 роки тому

    Dude, you just saved my life.. Owe you

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    @Aldosary0543 12 років тому

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

  • @AmanKumar-te8ft
    @AmanKumar-te8ft 5 років тому

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

  • @FURYofCURRIE
    @FURYofCURRIE 11 років тому

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

  • @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

  • @kevinshi270
    @kevinshi270 7 років тому +1

    Super good video, clear and easy to understand!!

  • @patrickborg509
    @patrickborg509 6 років тому +2

    I literally understood this more in this video than i have in 3 lectures with my lecturer. Thanks man

    • @patrickjmt
      @patrickjmt  6 років тому +1

      glad i could help you out!

  • @cookiesncream8490
    @cookiesncream8490 6 років тому

    Have a sudden quiz today and this really save my life thanks so much

  • @share-up3503
    @share-up3503 8 років тому

    you are amazing, thank you for helping me, i have a maths test next friday! much love from Portugal!

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    @leohnherschel3836 5 років тому +2

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  • @migs0338
    @migs0338 11 років тому

    Awesome method! needed this for my exam tomorrow

  • @millicentmarabe2324
    @millicentmarabe2324 2 роки тому

    thank you so much sir ..you literally just saved my life!!!!!!!

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    @zainabkhan8479 3 роки тому

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    Tomorrow I have my maths exam

  • @nafcatt8863
    @nafcatt8863 4 роки тому

    You have taught me what my professor couldn’t in the last 3 2-hour lectures

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    @saathwikhr7422 5 років тому

    Thank you bro. U explained better than my teacher

  • @jingyiwang5113
    @jingyiwang5113 2 роки тому +1

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

  • @davida6386
    @davida6386 7 років тому

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    @yousseffarouk7861 2 роки тому

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    @moonsunpan8772 11 років тому

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  • @DaLeR080
    @DaLeR080 9 років тому

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  • @abdullahisaahmed5366
    @abdullahisaahmed5366 10 років тому +4

    Simple and perfect...!!! Thanks man.