How To Find The Determinant of a 4x4 Matrix

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  • Опубліковано 5 жов 2024

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  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Рік тому +23

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    You've made this so simple, I can't believe how simple it is. Thank you so much.

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  • @appiahisaac9690
    @appiahisaac9690 4 роки тому +46

    Wow!
    This is the first time of learning 4x4 matrices. Thanks so much. You are the best tutor online.

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  • @SarcasticLampr4y
    @SarcasticLampr4y 4 роки тому +202

    Had a 3x3 on my maths exam last week. Thank you for all your information, got a High Distinction, top marks in my maths engineering class :D

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  • @georgesadler7830
    @georgesadler7830 2 роки тому +17

    MR. Organic Chemistry Tutor, thank you for an excellent video/lecture on Finding the Determinant of a 4x4 Matrix. This is a classic problem in old fashion Linear Algebra/Systems.

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    @cemonycrissmiller9337 3 роки тому +13

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  • @pockyrice7418
    @pockyrice7418 4 роки тому +13

    bruh im taking pre calc online and I literally came across this today, but it’s a 3x3 matrix and the HW is due today.
    I did not expect you to make a tutorial on how to do this. Freaking clutch man!!

    • @JagexAnarchy
      @JagexAnarchy 3 роки тому +1

      I'm also in pre-calc. The way the book teaches it makes it much more complicated. This is so much easier

  • @hadeerrashad5486
    @hadeerrashad5486 3 роки тому +15

    EXCELLENT explanations!! And thanks A LOT for telling us about the website

  • @sambozamamboza6508
    @sambozamamboza6508 Рік тому +2

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  • @chepaulinus2495
    @chepaulinus2495 4 роки тому +13

    Wow ,now I can find the determinant of a 4*4, thanks sir.

  • @VirtualTech
    @VirtualTech 2 роки тому +5

    Me an computer science student watching this after I forgot everything taught to us in 10th grade

  • @miz3567
    @miz3567 3 роки тому +115

    It may be good practice to draw straight lines for determinant instead of square brackets. 5*[A] means different thing to 5*|A|

    • @ayrthhhn
      @ayrthhhn 3 роки тому

      :V

    • @PenandPaperScience
      @PenandPaperScience 3 роки тому +8

      That is correct :)

    • @abdullahsehgal1614
      @abdullahsehgal1614 2 роки тому +3

      cut him some slack , like u wouldn't be here if u knew more then him

    • @aarohganjoo1676
      @aarohganjoo1676 2 роки тому +17

      @@abdullahsehgal1614 hey you have a point but proper notation is very important. A matrix and determinant are not the same thing, so it would be incorrect to use square brackets when computing a determinant

    • @nish3003
      @nish3003 2 роки тому +4

      @@abdullahsehgal1614 jeez, calm down dude, it was just a suggestion.

  • @adritobiswas1982
    @adritobiswas1982 2 роки тому +4

    I don't comment generally but I read in Class 7. In my school, Cramer's rule should be in class 9 or something like that. Even I understood your lectures that is 2×2, 3×3 and now this 4×4 one. If you think I am lying, then I swear to God.Amazing! Teach like this!!!

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    @ElBernardProfessional 2 місяці тому +1

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  • @chiviza
    @chiviza 8 місяців тому

    My professor speaks perfect english but I understood nothing when he showed this in the lecture. 40 seconds in with your video and I already get it. Thank you soooooo much.

  • @kefilwegabonakemo8960
    @kefilwegabonakemo8960 3 роки тому +4

    You explain better than my teacher🥂✨

  • @dermakol8543
    @dermakol8543 Рік тому +8

    Recommend a bit of gaussian elimination - if you add third row to first and third row multiplied by 2 to second and fourth, you will get a nice (0, 0, -1, 0) column and you only have to calculate a determinant of one 3x3 matrix.

    • @marcelukeje3510
      @marcelukeje3510 7 місяців тому

      It doesn't work that way.
      It only works for equations

    • @dermakol8543
      @dermakol8543 7 місяців тому

      Yeah, it does, adding a multiple of a row doesn't change anything. The other row operations do, but it is still just a scaling by constant you can keep track of.

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    At last I'm cleared of confusion💓📖

  • @NaiduRocks-xy9ft
    @NaiduRocks-xy9ft 3 місяці тому

    Solving by this method is heaven.tq man🙌

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    @upw4353 3 роки тому +1

    from ochem to biophysics this guy is always helping me out thanks

  • @anwar4227
    @anwar4227 4 роки тому +13

    One recommendation......you can use Sarrus rule for determinants and solve it quickly within 2 minutes

    • @yashjoshi2944
      @yashjoshi2944 4 роки тому

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    @amogusgusamo5591 6 місяців тому

    The best teacher. Thank you.

  • @seamusflannery3374
    @seamusflannery3374 2 роки тому

    This is a GREAT way to find determinants

  • @centric145
    @centric145 2 роки тому

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  • @Fasonlar2023
    @Fasonlar2023 Рік тому +1

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  • @nup_pun
    @nup_pun 3 роки тому +26

    or you can simply transform it into an upper triangular matrix by performing row-elementary operation and then by multiplying its diagonal elements we get the determinant.

    • @physician8683
      @physician8683 2 роки тому +3

      that's gaussian which is essentially better than cramer's but he's using cramer's rule

    • @nanananabatman7056
      @nanananabatman7056 Рік тому

      @@physician8683 hes not using cramer, or else he would replace the values with the result to get the values

    • @nanananabatman7056
      @nanananabatman7056 Рік тому

      with what do you multiply the diagonal ?

    • @noahsibahi-jackson8757
      @noahsibahi-jackson8757 Рік тому

      @@physician8683 No he is not, that isn't crammer's rule

  • @seanhsieh4149
    @seanhsieh4149 3 місяці тому

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    @revygoth 3 роки тому +1

    THANK YOU. Exam in less than 2 hours. Lets goo

  • @mrdracula7822
    @mrdracula7822 3 роки тому +2

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    @Resinart_and_caligraphy Рік тому

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    @farisanwari777 3 роки тому +1

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  • @sergosdeoliveros8033
    @sergosdeoliveros8033 2 роки тому +1

    a comment for the algorithm out of thankfulness

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    @Anduuu077 5 місяців тому

    very good, straight to the point video

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    @esarapuharika1685 2 роки тому +2

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    @cindyatuhaire 3 роки тому +2

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    @knkworld6765 2 роки тому

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  • @_ndot
    @_ndot 2 роки тому +2

    Explanation on the signs for each operation.
    Everything should be an addition and the sign comes from multiplying (-1)^(row-index + column-index). So, if you were to use the second row you should have:
    2 x ((-1)^(2+1)) x |minor at M2,1| + 5 x ((-1)^(2+2)) x |minor at M2,2| + ...
    2 x (-1) x |minor at M2,1| + 5 x (1) x |minor at M2,2| + ...
    -2 x |minor at M2,1| + 5 x |minor at M2,2| + ...
    This part gives you the sign for row 2 column 1: ((-1)^(2+1)) = -1.
    The easiest way to think about it, is to add the indices if its odd is - if its even is +.
    Row 2 Column 1 => 2 + 1 = 3 => odd -
    Row 2 Column 2 => 2 + 2 = 4 => even +
    Row 2 Column 3 => 2 + 3 = 5 => odd -
    Row 2 Column 4 => 2 + 4 = 6 => even +
    ...

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    @quintencraenen Рік тому +1

    Very helpful and explained perfectly!

  • @snooptech
    @snooptech 3 роки тому +1

    Thanks for letting me know the signs alternate

  • @Salamanca-joro
    @Salamanca-joro 4 місяці тому

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    @kingarayaankitff6942 2 роки тому +1

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    @happydong8086 3 роки тому +1

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    @MrWibbers 3 роки тому +1

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      @MrWibbers 3 роки тому

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    @masivuyedangazele7316 2 роки тому

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    @jomeltopiq5370 2 роки тому

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    @maimounah2001 3 роки тому +2

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    @jsrk265 2 роки тому +1

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    @niranjanakumar6638 3 роки тому +1

    It was very beneficial
    Tysm❤️

  • @moussachouka5305
    @moussachouka5305 6 місяців тому

    Your method is vero great congratulation

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    @enashameed471 3 роки тому +1

    Thanks جزاك الله خيرا ❤

  • @davidmurphy563
    @davidmurphy563 9 місяців тому +1

    That's the full way! You can use row reduction to add more zeros... But you have to keep track of the operations and sdd a coefficient for each type.
    Or, you know, use a function.

  • @khanmengui3709
    @khanmengui3709 4 роки тому

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    @glorytuesday1034 3 роки тому

    thank so much sir ,i understand better now

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    @Karimzada_091 2 роки тому

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    @OseiVivian-r3y 6 місяців тому +1

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