❖ Finding the Determinant of a 3 x 3 matrix ❖

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  • Опубліковано 28 вер 2024
  • 📚 Finding the Determinant of a 3x3 Matrix: Step-by-Step Guide 🧮
    In this video, I walk you through the basic formula for finding the determinant of a 3x3 matrix. We’ll compute the determinant of a specific matrix by breaking it down into smaller 2x2 determinants for clarity.
    🚀 What you’ll learn:
    The general procedure for calculating the determinant of any 3x3 matrix.
    A quick trick to speed up finding the determinant, although we’ll focus on the traditional method to ensure a solid understanding that involves cofactors.
    How understanding the breakdown into 2x2 matrices helps in more complex linear algebra problems.
    This step-by-step guide is ideal for students learning linear algebra, preparing for exams, or anyone wanting to solidify their matrix computation skills. Be sure to check out my other videos for more on matrices, inverses, and solving systems of equations!
    👍 Don’t forget to like, subscribe, and hit the notification bell for more math tutorials! 🔔✨
    Watch now to master finding the determinant of a 3x3 matrix!
    #Maths #LinearAlgebra #Determinants #InverseMatrix #RowReductionMethod #InverseOfMatrices #SystemOfLinearEquations #Algebra #MatrixDeterminants #MatrixMath #EducationalContent #STEM #MathTutorial

КОМЕНТАРІ • 1,2 тис.

  • @patrickjmt
    @patrickjmt  5 років тому +261

    Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other!
    Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!

    • @saurabhsingh6325
      @saurabhsingh6325 4 роки тому +6

      Wasn't this video posted in 2009?

    • @nitinvadel849
      @nitinvadel849 4 роки тому +2

      What is crammer rule

    • @saurabhsingh6325
      @saurabhsingh6325 4 роки тому

      It's states the solutions of 3 equations

    • @saurabhsingh6325
      @saurabhsingh6325 4 роки тому +1

      Bhai JEE MAIN aA raha hai...brace yourselves

    • @landor6523
      @landor6523 4 роки тому +1

      For an example if the first row was 1 -2 -4 would it be +1|?| -2|?| +4|?| or not cause i'm confused by that part ?

  • @patrickzielinski7769
    @patrickzielinski7769 3 роки тому +668

    Your almost 12 year old videos are still helping students around the world. Thank you so much!

  • @patrickjmt
    @patrickjmt  14 років тому +252

    it seems to help so many people, and people seem so grateful in return.
    i am happy that i have something that i can share with people that makes them feel better!

  • @johnallen1883
    @johnallen1883 8 років тому +680

    you deserve my professors paycheck

  • @smillieboy07
    @smillieboy07 12 років тому +8

    You have taught me more in less than 7 minutes than my lecturer has taught me in 2 months, thank you!

  • @hudaabbas1700
    @hudaabbas1700 10 років тому +88

    Thanks a lot I wish my teacher would explain things like u, I swear we r not dumb but teacher don't know how to explain things
    You r a life saver

    • @gibraanbutt6062
      @gibraanbutt6062 6 років тому +3

      Huda Abbas I thought i was dumb until I started learning online😄 I can relate to this😂

    • @MKFilms21
      @MKFilms21 6 років тому

      You r right

    • @Art-fn7ns
      @Art-fn7ns 5 років тому +1

      > "not dumb"
      > "u" "r"
      > no periods
      > "we r not dumb" "I swear"

    • @angryprogrammer7788
      @angryprogrammer7788 5 років тому +5

      @@Art-fn7ns you do realize that the og comment is 4 years old, right?

  • @patrickjmt
    @patrickjmt  14 років тому

    @dajakesta1234 no, you are not allowed to ask.

  • @patrickjmt
    @patrickjmt  15 років тому +4

    yes, i agree!
    i was debating which way i would show first....
    i decided on this method though cause i think it ends up being more insightful : )
    however, it may also be more computationally cumbersome, but not by very much i think

  • @patrickjmt
    @patrickjmt  14 років тому +2

    @Akarashl not sure what you mean; i think you are talking about when i find the determinant of each of the resulting 2x2 matrices though

  • @patrickjmt
    @patrickjmt  12 років тому +8

    thanks for watching for so long :)

  • @yens086
    @yens086 10 років тому +1

    why on earth will some people dislike this video thanks PATRICKJMT you av helped me passed my courses from my first year till my third year i love u

  • @phethohlubi2530
    @phethohlubi2530 7 років тому +96

    God bless you Patrick, great job..

  • @shivanshkhandelwal859
    @shivanshkhandelwal859 2 роки тому +1

    thus 2 minute crashcourse helped jog my memory for my hsc boards..these simple tutorials help a lot of students around the world .thankyou

  • @dylanmetzdorf
    @dylanmetzdorf 10 років тому +39

    you my friend, are a lifesaver

    • @dev.prateek5781
      @dev.prateek5781 3 роки тому

      U commented 7 years ago, I hope u come back to see this reply 😁 , maybe it will be nostalgic

    • @dylanmetzdorf
      @dylanmetzdorf 3 роки тому +3

      @@dev.prateek5781 Oh my Gosh, Having just graduated college and started working my first job.... this was definitely nostalgic

    • @dev.prateek5781
      @dev.prateek5781 3 роки тому

      @@dylanmetzdorf i hope it made u smile😉 and you living a happy life. Good luck for future😁

  • @hubertninnymuggins
    @hubertninnymuggins 6 років тому

    The explanations that my professor gave and my math lab were useless. After I watched this I finished my homework in less than 10 minutes. Thanks man!

  • @IrisPark98
    @IrisPark98 11 років тому +57

    The shit we all students have to deal with.....

    • @Alhussainba
      @Alhussainba 6 років тому +13

      Iris Park hope you're a doctor by now

    • @mim073
      @mim073 6 років тому

      Lol

    • @jimbb3821
      @jimbb3821 6 років тому +1

      are u though?

    • @vedangbohra4562
      @vedangbohra4562 3 роки тому +1

      Are you a doctor now?

    • @IrisPark98
      @IrisPark98 3 роки тому +8

      @@vedangbohra4562 hell no

  • @melissarainchild
    @melissarainchild 4 роки тому +1

    The way you explain is is so relaxed and chill, I just like to listen to it WHILE I study :)

  • @patrickjmt
    @patrickjmt  14 років тому +1

    @inneruniverse17 watch my calculus videos and i will (partly)

    • @hamayoonkhaan7084
      @hamayoonkhaan7084 3 роки тому

      Hi.
      U wrote -6 on 1 and then after -6 the last u wrote +4 ? Why?

  • @Gluecow
    @Gluecow 10 років тому +1

    thanks my teacher did a bunch of problems w/ Vectors using matrices but most of our class didn't know how to do matrices, so he told us we have to learn it on our own, teacher of the year for sure.

  • @AlexandrosIgnatiou
    @AlexandrosIgnatiou 10 років тому +1

    Thank you! Thank you! Thank you! I am extremely grateful you are making videos on UA-cam!

  • @1stPersonTutor
    @1stPersonTutor 3 роки тому

    I found this video back in 2015, and I'm revisiting it again 5 years later in the midst of the Covid era of teaching. Thanks again. You deserve all the credit for having the best video on finding the Determinant of a 3x3 Matrix. 🙇‍♂️🙇‍♂️🙇‍♂️🙇‍♂️

  • @mandisamkhize4475
    @mandisamkhize4475 9 років тому +24

    why aren't you my lecture? You the best Patrick

  • @longfenglim
    @longfenglim 13 років тому

    This is excellent, because my book teaches the determinants as the sum of the entries of a particular i-th row or j-th column multiplied by its corresponding cofactors- and then teaches the cofactors as the determinant of the whole lot times negative one to the power of the i plus j, esentially a circular definition. Thank you very much for it.

  • @_a__abdulrahman
    @_a__abdulrahman 7 місяців тому

    14 years ago and still beneficial. Good job. Mr.

  • @jonathang4963
    @jonathang4963 10 років тому +3

    Thank you so much, I couldn't follow my teacher's lecture. If there is a way I could repay you I would.

  • @dramageek1213
    @dramageek1213 13 років тому +1

    Thanks so much! This was so helpful. Our teacher had us watch this in class when he was absent and it helped so much!

  • @thanabaljeyasree5305
    @thanabaljeyasree5305 6 років тому +1

    Patrick, You're awesome. I really understood your method of teaching. Thanks alot Patrick!

  • @richardaddison15
    @richardaddison15 8 років тому +3

    That's a great tutorial. Very helpful

  • @iamtheboss8065
    @iamtheboss8065 3 роки тому

    I am watching in 2021 right now, and I just noticed that this video was published 12 years back!!!!! thank you sir, superb explanation by the way!!!

  • @patrickjmt
    @patrickjmt  14 років тому

    @fateater77777 yes, that would be acceptable!

  • @aelw23
    @aelw23 12 років тому

    A million thanks... you're a lifesaver. My prof is a good person, but his handwriting is mysterious, and he has one of the heavier accents I've come across so far...

  • @faisalzakari6489
    @faisalzakari6489 2 роки тому

    Wow 13 years ago. I have a very important exam tomorrow and I’m learning this today, thank you very much. Couldn’t have learnt it in class

  • @lomeshpawar5232
    @lomeshpawar5232 3 роки тому +5

    Anyone from India 🇮🇳🙂

  • @alanoreilly1747
    @alanoreilly1747 5 років тому

    You explained to me in 6 minutes what my lecturer couldnt explain to the class in 3 hours take my like good sir.

  • @kaioneal6160
    @kaioneal6160 5 років тому

    I have not taking a math class in a year, watching these videos are very nostalgic.

  • @retrohd1_
    @retrohd1_ 3 роки тому

    I wasted half hour doing this for each row and then realized that something didn’t seem right 😂😓
    Thanks for the video! You’re a life saver!

  • @gyulboxing
    @gyulboxing 2 роки тому

    Thank you for taking the process step by step and making it intuitive. It helped me a lot.

  • @robdog7731
    @robdog7731 6 років тому

    The covering of rows and coloms is surprisingly helpful

  • @carolynlambert8797
    @carolynlambert8797 6 місяців тому +1

    you helped me in college long time ago thanks so much!

  • @sia7001
    @sia7001 8 років тому +3

    why do we only use the first row?

    • @nathanherbertson8987
      @nathanherbertson8987 8 років тому

      I think you can use any row, in practice use the row with the most zeros as there's less work to do.

    • @sia7001
      @sia7001 8 років тому

      +Nathan Herbertson okie thanks 😁

    • @Lockerd23
      @Lockerd23 8 років тому +1

      Correct! It doesn't matter which row or even column you use :)
      Just keep in mind the pattern of + and -
      + - +
      - + -
      + - +

    • @Rere27420
      @Rere27420 8 років тому

      when do we use the rule A ij = -1 Raised to the power i + j multiply by M ij

    • @Rere27420
      @Rere27420 8 років тому

      I have one example by this rule

  • @theonaidu6274
    @theonaidu6274 7 років тому

    patrick if it werent for you id not have understood anything i did this semester! you the best!

  • @PeterBJams
    @PeterBJams 14 років тому

    Wow, this is crystal clear. My prof speeds through so fast you can't even get the matrix written down before he is erasing. This isn't so complicated afterall.

  • @rodyotaku8756
    @rodyotaku8756 7 років тому +4

    he is left-handed, right?

    • @tanishashah3215
      @tanishashah3215 7 років тому +11

      yes he is. but it doesn't matter.

    • @blu9168
      @blu9168 5 років тому

      +Tanisha shah 😂

  • @patrickjmt
    @patrickjmt  14 років тому

    @LeuJinx when i wake up each morning, i look in the mirror, and i tell myself that 10 times. also my math fan-girls that i keep around also tell me, ten times each. it is a nice way to start my morning.

  • @ramyasuvarna992
    @ramyasuvarna992 5 років тому

    Thank you so much for making this video... this is really useful and very easy..I'm gonna write my math exam tomorrow... And after watching this my confidence has increased..

  • @jennifercestina5805
    @jennifercestina5805 12 років тому

    this tutorial of yours is very helpful for students like me.. thanks a lot.. MORE POWER!!! :)

  • @KIETGIANGDBZ
    @KIETGIANGDBZ 13 років тому

    I'm in honors trig/precalculus and i'm a junior or 11th grader... you are so much better than my teacher.

  • @lers101
    @lers101 14 років тому

    thanks patrickJMT, just started back at grad school and am thankful for the refresher (even if i do default to my TI soon)... matrix math was a long time ago!

  • @chemistrykicksass
    @chemistrykicksass 11 років тому

    Man, you are the greatest! You helped me so much with this video and that´s not the first time. Keep up with the good work! Greetings from Vienna/Austria.

  • @MsBasith
    @MsBasith 12 років тому

    thank you ,
    you had helped me for my today's university exam
    i thank you like a million time

  • @LilMizBri1
    @LilMizBri1 12 років тому

    Thanks. My algebra teacher didnt explain it clearly but you helped me alot. :)

  • @patrickjmt
    @patrickjmt  12 років тому

    @MonikadeVilette glad i could help :)

  • @TechSunnimuslim07860
    @TechSunnimuslim07860 5 років тому +2

    Thnx dear. Lot of luv from Bihar India🇮🇳🇮🇳😎😎

  • @ml6008
    @ml6008 13 років тому

    Thanks for the video. Believe it or not I am a Diff Eq student who never learned matrices. This is a huge help when computing Wronskians.

  • @arielbaeza1
    @arielbaeza1 10 років тому

    Thank you so much patrickJMT all of your videos are extremely helpful.

  • @mkusasakala3861
    @mkusasakala3861 10 років тому

    i like the idea of covering the cancelled rows and columns

  • @RichieAlek
    @RichieAlek 14 років тому

    Dude you ROCK! It's because of this method (which i learned here) that i got all of these questions correct on my final!!!

  • @aarushiacharya8790
    @aarushiacharya8790 Рік тому

    Wow its already 14 yrs but it helped me
    Thank you so much!❤

  • @Demogooo
    @Demogooo 2 роки тому

    Holy moly! Thank you for the video, it literally saved me from a huge headache. :)

  • @MAR_10-x5w
    @MAR_10-x5w Рік тому

    holy this is very easy to understand and watch while not too long.

  • @ElitistMagi
    @ElitistMagi 14 років тому

    dude thanks a lot got exam in an hour this video was really helpful!!! much love brah!

  • @zangetsuzanpakuto5221
    @zangetsuzanpakuto5221 6 років тому

    THANKS SO MUCH THIS EXPLANATION MADE IT SOME MUCH MORE CLEAR THAN MY TEACHER

  • @MsVictoriousrocks
    @MsVictoriousrocks 11 років тому

    Thanks man . You helped me alot . I'm not from the US and this type of questions wont be coming out in my exams . But i'm planning to live in the US one day . Maybe in the future

  • @vee361-e1c
    @vee361-e1c 7 років тому

    Thanks so much Patrick, you saved me in calc 2 and you're saving me again in calc 3

  • @Cassielball
    @Cassielball 8 років тому

    My exam is tomorrow. You have my eternal grattitude

  • @MeritodaCostaBelo
    @MeritodaCostaBelo 11 років тому

    I suppose -96 for calculation. anyhow I thank you very much for your explanation. you're a good instructor ever. you're one of the best teacher.

  • @tonyayad5629
    @tonyayad5629 3 роки тому

    Almost 13 years of people loving this video

  • @MandyBedRock
    @MandyBedRock 14 років тому

    thank you very much....been trying to grasp this in lecture but it was just too overwhelming, so once again thank you.

  • @carbonurbuddy3456
    @carbonurbuddy3456 4 роки тому

    Thanks a lot looked at my maths book for 15 mins didn't get a thing, and Walla here I get it in one time

  • @srishtiaryamona
    @srishtiaryamona 5 років тому

    Thank you for teaching us the easiest way possible. I seriously don't know what's wrong with these dislikers, I don't think there couldn't be any possible easier explanation to this topic!

  • @LoxagosSnake
    @LoxagosSnake 11 років тому

    Thanks dude, pretty quick explanation! Saved me a lot of time because I need this for some Analytic Geometry stuff.

  • @Sethstrat
    @Sethstrat 11 років тому

    it's always a11 is +, a12 is -, a13 is + for the setup. If, for example, a11 itself is a negative value it will be + (-a11). If a12 is a negative number, then it will be - (-a12); if a13 is a negative number, then it will be +(-a13)

  • @RainbowVeins99
    @RainbowVeins99 14 років тому

    THANK YOU! No one has been able to explain this to me like you do!

  • @edwinsoccergoalie240
    @edwinsoccergoalie240 12 років тому

    You guys are freaking awesome I'm in alg 2/ trig honors and that class is so hard thanks for making this as clear as possible I've understood this in about 10 minutes compared to an hour in class!!!!!!!!! You guys hella beast!!!!!!

  • @yousha.lol1
    @yousha.lol1 8 місяців тому

    14 years old vid and still its helping students like me stay safe bro

  • @starlitz_328
    @starlitz_328 14 років тому

    thank you sooooooo much!!! Your videos are the reason I'm passing algebra ll this year.

  • @michieldrost9396
    @michieldrost9396 11 років тому

    Is this operation also related to the cross product in any way, or is it just a similarly looking operation? Thanks, clear video.

  • @BeachBunny12345
    @BeachBunny12345 12 років тому

    Hi Pat! In an example in my book, to find the determinant, instead of covering up the first row (a11, a12, a13), they cover up the second row (a21, a22, a23). Do you know why?

  • @DDoesT
    @DDoesT 5 років тому

    For the second example: When setting up, are you not supposed to subtract 1|matrix| -6|matrix|-4|matrix|? How come the +4|matrix| instead?

  • @paulelling851
    @paulelling851 7 років тому

    This helps a lot! Thanks for also using an example to instantly apply the new learned math

  • @415HolyGuy
    @415HolyGuy 13 років тому

    Thanks, Great informative video. Calmly presented in a thorough manner. Much appreciated!

  • @T725db
    @T725db 12 років тому

    Perfect. My teacher taught this over a series of 3 days. You taught it in a series of 6 MINUTES!!!!!! Thank you so much.

  • @dada00321
    @dada00321 5 років тому

    Clear. Thx for your teaching from Taiwan.

    • @patrickjmt
      @patrickjmt  5 років тому

      you are welcome from Texas!

  • @damiccathedesigner
    @damiccathedesigner 12 років тому

    Why isn't my math course this simple! Why do they have to make things so complicated....THANKS A TON!!!!!!!!!!!!!!!!!!!

  • @summercures2
    @summercures2 14 років тому

    If when there is a negative number in the area where it's supposed to be negative by default, does that number turn positive?

  • @babydolldiorable
    @babydolldiorable 11 років тому

    Thank you so much for taking the time to explain this and post it! You've helped me a ton.

  • @bethanylindsey2735
    @bethanylindsey2735 8 років тому

    If a problem specifically asks for A12, do you work out the problem any differently?

  • @chawankawa4506
    @chawankawa4506 8 років тому +1

    You did greatly! It was very helpful :)

  • @مسعدالشعب
    @مسعدالشعب 11 років тому

    Thanks a lot!!! This really helped! I have been stuck with it for a long time but, know since I watched the video I'm able to solve any problem!! Thanks :)

  • @martinmike9581
    @martinmike9581 7 років тому +1

    such simple explanation.made it real easy. thanks

  • @twixcjc1985
    @twixcjc1985 14 років тому

    You make this soo simple! Thanks a lot! your videos are so helpful!

  • @zayde199
    @zayde199 10 років тому

    Thank you very much! I wish that you were my teacher.

  • @snowboardgoddess7
    @snowboardgoddess7 11 років тому

    You are a God.... seriously i think you work miracles!!! THANK YOU!!!!

  • @captainnaeem4433
    @captainnaeem4433 5 років тому

    Thank you so much Sir.
    It was so complicated, but you made it too easy.

  • @akshat_study
    @akshat_study Рік тому

    studying for board exams tommorow and stumbled upon this masterpiece

  • @thaongaojoyrana1355
    @thaongaojoyrana1355 2 роки тому

    Thank you for making it very simple to understand

  • @HunterkillerTV
    @HunterkillerTV Рік тому

    I have some question. If a12 in setA is negative(-6), when we have to calculate detA. We have to change -6 to 6 isn’t it?

  • @dkdasniper797
    @dkdasniper797 2 роки тому

    thanks a lot. i got my AI exam tomorrow this will definitely help me

  • @killermonster555
    @killermonster555 11 років тому

    really helpful video. I despise matrices, but they're really becoming clear now.

  • @anilgoud9034
    @anilgoud9034 6 років тому

    u made it simple
    thank u patrick