❖ 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
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!
Wasn't this video posted in 2009?
What is crammer rule
It's states the solutions of 3 equations
Bhai JEE MAIN aA raha hai...brace yourselves
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 ?
Your almost 12 year old videos are still helping students around the world. Thank you so much!
Long live online education :)
They really are
Yes .....
@@everythingbeautiful9288
I love u darling... 💋💋💋
I m from India...
Those ads saying "are those videos from 2006 really helping?"... yes, very much
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!
Thanks sir!😄
11 years ago
:)
Yes it helped me a lot
Thank you sir
you deserve my professors paycheck
Thank
you
very
very
much
You have taught me more in less than 7 minutes than my lecturer has taught me in 2 months, thank you!
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
Huda Abbas I thought i was dumb until I started learning online😄 I can relate to this😂
You r right
> "not dumb"
> "u" "r"
> no periods
> "we r not dumb" "I swear"
@@Art-fn7ns you do realize that the og comment is 4 years old, right?
@dajakesta1234 no, you are not allowed to ask.
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
@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
thanks for watching for so long :)
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
God bless you Patrick, great job..
thanks!
You are good
thus 2 minute crashcourse helped jog my memory for my hsc boards..these simple tutorials help a lot of students around the world .thankyou
you my friend, are a lifesaver
U commented 7 years ago, I hope u come back to see this reply 😁 , maybe it will be nostalgic
@@dev.prateek5781 Oh my Gosh, Having just graduated college and started working my first job.... this was definitely nostalgic
@@dylanmetzdorf i hope it made u smile😉 and you living a happy life. Good luck for future😁
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!
The shit we all students have to deal with.....
Iris Park hope you're a doctor by now
Lol
are u though?
Are you a doctor now?
@@vedangbohra4562 hell no
The way you explain is is so relaxed and chill, I just like to listen to it WHILE I study :)
@inneruniverse17 watch my calculus videos and i will (partly)
Hi.
U wrote -6 on 1 and then after -6 the last u wrote +4 ? Why?
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.
Thank you! Thank you! Thank you! I am extremely grateful you are making videos on UA-cam!
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. 🙇♂️🙇♂️🙇♂️🙇♂️
why aren't you my lecture? You the best Patrick
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.
14 years ago and still beneficial. Good job. Mr.
Thank you so much, I couldn't follow my teacher's lecture. If there is a way I could repay you I would.
Thanks so much! This was so helpful. Our teacher had us watch this in class when he was absent and it helped so much!
Patrick, You're awesome. I really understood your method of teaching. Thanks alot Patrick!
That's a great tutorial. Very helpful
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!!!
@fateater77777 yes, that would be acceptable!
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...
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
Anyone from India 🇮🇳🙂
Yhh
You explained to me in 6 minutes what my lecturer couldnt explain to the class in 3 hours take my like good sir.
I have not taking a math class in a year, watching these videos are very nostalgic.
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!
Thank you for taking the process step by step and making it intuitive. It helped me a lot.
Hlo bro
The covering of rows and coloms is surprisingly helpful
you helped me in college long time ago thanks so much!
why do we only use the first row?
I think you can use any row, in practice use the row with the most zeros as there's less work to do.
+Nathan Herbertson okie thanks 😁
Correct! It doesn't matter which row or even column you use :)
Just keep in mind the pattern of + and -
+ - +
- + -
+ - +
when do we use the rule A ij = -1 Raised to the power i + j multiply by M ij
I have one example by this rule
patrick if it werent for you id not have understood anything i did this semester! you the best!
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.
he is left-handed, right?
yes he is. but it doesn't matter.
+Tanisha shah 😂
@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.
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..
this tutorial of yours is very helpful for students like me.. thanks a lot.. MORE POWER!!! :)
I'm in honors trig/precalculus and i'm a junior or 11th grader... you are so much better than my teacher.
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!
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.
thank you ,
you had helped me for my today's university exam
i thank you like a million time
Thanks. My algebra teacher didnt explain it clearly but you helped me alot. :)
@MonikadeVilette glad i could help :)
Thnx dear. Lot of luv from Bihar India🇮🇳🇮🇳😎😎
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.
Thank you so much patrickJMT all of your videos are extremely helpful.
i like the idea of covering the cancelled rows and columns
Dude you ROCK! It's because of this method (which i learned here) that i got all of these questions correct on my final!!!
Wow its already 14 yrs but it helped me
Thank you so much!❤
Holy moly! Thank you for the video, it literally saved me from a huge headache. :)
holy this is very easy to understand and watch while not too long.
dude thanks a lot got exam in an hour this video was really helpful!!! much love brah!
THANKS SO MUCH THIS EXPLANATION MADE IT SOME MUCH MORE CLEAR THAN MY TEACHER
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
Thanks so much Patrick, you saved me in calc 2 and you're saving me again in calc 3
My exam is tomorrow. You have my eternal grattitude
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.
Almost 13 years of people loving this video
thank you very much....been trying to grasp this in lecture but it was just too overwhelming, so once again thank you.
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
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!
Thanks dude, pretty quick explanation! Saved me a lot of time because I need this for some Analytic Geometry stuff.
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)
THANK YOU! No one has been able to explain this to me like you do!
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!!!!!!
14 years old vid and still its helping students like me stay safe bro
thanks homie
thank you sooooooo much!!! Your videos are the reason I'm passing algebra ll this year.
Is this operation also related to the cross product in any way, or is it just a similarly looking operation? Thanks, clear video.
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?
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?
This helps a lot! Thanks for also using an example to instantly apply the new learned math
Thanks, Great informative video. Calmly presented in a thorough manner. Much appreciated!
Perfect. My teacher taught this over a series of 3 days. You taught it in a series of 6 MINUTES!!!!!! Thank you so much.
Clear. Thx for your teaching from Taiwan.
you are welcome from Texas!
Why isn't my math course this simple! Why do they have to make things so complicated....THANKS A TON!!!!!!!!!!!!!!!!!!!
If when there is a negative number in the area where it's supposed to be negative by default, does that number turn positive?
Thank you so much for taking the time to explain this and post it! You've helped me a ton.
If a problem specifically asks for A12, do you work out the problem any differently?
You did greatly! It was very helpful :)
I'm from india
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 :)
such simple explanation.made it real easy. thanks
You make this soo simple! Thanks a lot! your videos are so helpful!
Thank you very much! I wish that you were my teacher.
You are a God.... seriously i think you work miracles!!! THANK YOU!!!!
Thank you so much Sir.
It was so complicated, but you made it too easy.
studying for board exams tommorow and stumbled upon this masterpiece
Thank you for making it very simple to understand
Hlo bro
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?
thanks a lot. i got my AI exam tomorrow this will definitely help me
really helpful video. I despise matrices, but they're really becoming clear now.
u made it simple
thank u patrick