Cramer's Rule - 3x3 Linear System

This precalculus video tutorial provides a basic introduction into cramer's rule. It explains how to solve a system of linear equations with 3 variables using determinants of 3x3 matrices.
Introduction to Matrices: • Intro to Matrices
Adding and Subtracting Matrices:
• Adding and Subtracting...
Scalar Multiplication of Matrices:
• Scalar Multiplication ...
Solving Matrix Equations:
• Solving Matrix Equations
Multiplying Matrices:
• Multiplying Matrices
__________________________________
Gaussian Elimination & Row Echelon Form:
• Gaussian Elimination &...
Gauss Jordan Elimination:
• Gauss Jordan Eliminati...
Gaussian Elimination With 4 Variables:
• Gaussian Elimination W...
Inverse of a 2x2 Matrix:
• Inverse of a 2x2 Matrix
Inverse of a 3x3 Matrix:
• Inverse of a 3x3 Matrix
__________________________________
Determinant of 2x2 and 3x3 Matrix:
• Determinant of 3x3 Mat...
Determinant of 4x4 Matrix:
• How To Find The Determ...
Cramer's Rule - 2x2 Linear System:
• Cramer's Rule - 2x2 Li...
Cramer's Rule - 3x3 Linear System:
• Cramer's Rule - 3x3 Li...
___________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Next Video: ruclips.net/video/YWHyovdHqkg/видео.html

[@SP-ge6kv]

I never add comments but I just wanted to say that you've literally had my back since day 1. In high school I have been watching your chemistry videos for years, and your maths ones too. Now, years later, while already in my second year of university studying economics, you still somehow manage to help me with so many things. I genuinely cannot thank you enough.

[@taladabbagh1827]

Ok

[@kylewilhite4162]

Same dude!!!

[@jamorant7132]

Fr

[@endy_011]

amogus

[@wonderman8537]

Patreon

[@loganmassee4933]

My man, I have been pursuing an Electrical Engineering degree since 2017. You've literally saved me during home works, tests, and quizzes. From Trig, to calculus 3, to linear algebra, to DiffEq, and now even into systems and signals! You have helped me and so many other people dude! You're quite possibly the most underappreciated academic asset the information age has ever seen! THANK YOU!!!

[@iluvyunie]

hope you're still going stronk dude

[@epikman7073]

There’s a fucking calculus what. Man Idk what’s ahead of me I’m in Alg 2 rn 😢

[@TripleC_Lifts]

@@epikman7073 theres a 5 & 6 they like to call advanced cal 1& 2😭

[@yeoslovelyblu]

​@@epikman7073😭😭

[@Katygracelee]

​@@epikman7073 oh geometry, trigonometry, pre-calculus, calculus, calculus 2, calculus 3, linear algebra, and differential equations.

[@freudbrahms254]

You accompany me in the loneliest of study times, much love, keep it up, no homo.

[@likea24inchrim]

sus

[@kidus_tv]

sus

[@freudbrahms254]

Screw you guys

[@NormanYeung19]

pause

[@frijolex2509]

hits too close to home :,,)

[@_Only.one.me_]

This channel has saved a lot of lives and it’s still Savin 🤲🏽

[@caleborg5688]

This made a lot more sense than the pages of notes we got from our teacher... thank you

[@cecilianyangu6790]

I agree with you...
The notes I Also received didn't make sense

[@neilandrews4097]

yes

[@cryptotare]

You're right! I also came here because this person first clear basics and then tell rules or something else. In this way it's easy to remember

[@whatafinese561]

My lecture is an ass he keeps the notes for himself

[@christianabrokwa6780]

Facts

[@jar01usmc]

"The Organic Chemistry Tutor" ....my math and physics savior. Keep it up!

[@NotJoseO]

This guy is one of the most important persons in this nation. The government should pay him he’s carrying the whole country at this point. I was in the library the other day and listened to his voice because someone was watching a video. Now I’m here watching one of his videos. Been helping me since high school. This also proves professors should do a better job teaching 😂.

[@nobodyspecial6799]

You have literally saved me. Thanks to you I actually have a chance of graduating in December! Bless you. Keep up the wonderful work

[@oreokid6882]

Hey how the graduation thing going?

[@FarooqAhmadiub]

ruclips.net/video/6ucjkUn35Ys/видео.html

[@promptlyjoebrown4305]

I can always find a better explanation here than from any of the math teachers or professors that I have ever had. I study Computer Engineering and you've helped me through every calculus and electrical engineering course, I don't even take chemistry.

[@mango6512]

I can’t explain how much more helpful this is than my actual lectures

[@meatball5544]

Found this channel during my school exam days, then again at college exam days, then again at my university entrance exam, then again during my 1, and 2 years, and now my exams are here again, and so is your channel.
Just wanted to say, you are doing something that is highly appreciated by all students and non-students. Thank you!

[@matte_molli]

someone actually thought about this... like Cramer was like okay im just gonna put all these numbers her select one delete the others multiply like that, then add them and in the end exchange a with d b with d and c with d and there's the answer

[@rubeneduardooseguedagomez8303]

@Javier Concepción wrong, he was high as fuck, all mathematicians were and are high as fuck

[@Matt-ii7hf]

@@rubeneduardooseguedagomez8303 Yes, this man did a hit of PCP, fought off the thought police, and solved this system of equations

[@chemist-man]

The best channel about chemisty
I recommended all students in my university to watch this channel
Igot high mark in (innorganic) when.i studied on your videos

[@neilandrews4097]

yes

[@mahimmarufuzzaman3588]

Not only chemistry this man knows everything

[@wytemusicinc987]

Nicee

[@isaactiwa5923]

M having exams this morning...and this tutiorial is making me feel I can do anything..I'm so glad I came across this..much love ..

[@pjisnotok4146]

This guy is my savior. My math teacher doesn’t bother to teach, so this saves my ass. (Seriously. She gives us packets then sits down and reads.)

[@putin_navsegda6487]

basically, it's how it works in real life. Teacher gives you themes and some general direction and after it's up to you to look for a good source and understand it. If ya not agree probably math is not your thing.

[@jacobfeinauer6487]

My teachers were not explaining this well, thanks for the straightforward and clear guide.

[@manuelvalentine7905]

this guy taught me a whole 7 day lesson in like 14:30 mins

[@ahmeddler]

Hahaha me too

[@joyjamani7281]

More like two weeks 😂😂.

[@MajidAoulad]

So simple and clear. His voice is of a good person. Math is easy here

[@sabex_og]

Anyone thinking if this video actually explains. My man, this is the video that only can explain the topic clearly to you. A lifesaver.

[@flopper_tropper9813]

Your videos never disappoint. You are a life saver 👌

[@rodduke2040]

I though Cramer's rule will be faster but damn it is longer... I suggest for those who want to resolve 3*3 to do x=A-1*b where A-1=ajoint(A)/determinant(a)

[@henrytumbusch4628]

This just saved me lots of stress ngl; you explained it so much better than my professor lol

[@aidankreltszheim3599]

I have been re watching my lecture for a couple of hours not understanding. I watch your video once and it all makes sense. Thank you so much.

[@samaawagih7272]

I love this man with my whole heart. I have been watching your videos from my senior year at high school and now I am a third-year Computer Science student. Thank you so much for your help!!!

[@Baldy8653]

You sir are a hero to college students worldwide!

[@nadiner5947]

WHAT!!! My brain just went to Timbuktu. I will keep watching and practicing. Thank you.

[@candrashanicepedro6209]

Your videos are so helpful, you have no idea the impact you're videos have had on my studies and furthering my studies... you are a star and truly grateful to have come across your RUclips channel.🙏

[@anasmikail9276]

you saved me

[@catalyzt7162]

absolute legend

[@neilandrews4097]

yes

[@catalyzt7162]

@@neilandrews4097 yes

[@neilandrews4097]

@@catalyzt7162 lmao nice

[@neilandrews4097]

@@catalyzt7162 didnt think you would respond

[@catalyzt7162]

@@neilandrews4097 he helped me do well in my maths test.

[@hydreox1911]

Literal LEGEND!!! Helped me with my maths assignment.

[@shaoi725]

best example of cramer's rule applied on linear system on the internet, very well explained, thank you.

[@yuushiade]

Thank you so much for the explanation. It was easy to understand. You never know how helpless I felt before.

[@gnsn5441]

I'm in 7th grade and I just started learning this today, and this video helped so much with the hw, tysm!

[@nickballas4729]

Bruh you learning this in 7th grade?

[@imsoundish]

I doing this in 9th and thought it was semi difficult

[@gnsn5441]

Nick Ballas lol it’s quite painful, I took a summer course

[@gnsn5441]

SoundlessDestiny it is really hard

[@Riverish]

i learned it in 7th too. i'm in calculus now, and thought that i might review it for fun.

[@openebolowa4843]

Thank you so much, best teacher on RUclips ❤❤

[@jjcadman]

Very nicely explained.
One minor quibble: you are using the notation for matrices (the square brackets: "[" and "]") when you should be using the notation for determinants (the straight lines, or pipes: "|" and "|"). But everything else was great! 👍

[@amoghreddy8885]

grow up

[@viculty4724]

What????? It’s literally the correct thing, brackets mean something completely different (greatest integer expression)

[@amoghreddy8885]

grow up

[@AclinGG]

@@amoghreddy8885 teacher literally said he'd fail us in the exam for that you stupid cunt

[@michelletowett377]

Hello Teacher ....I major in math and Chemistry in University of Eastern Africa baraton in Kenya .. you've always have my back 🇰🇪👍...Thank you

[@nkumbusinkamba5839]

Just hours before my exam! This man is a lifesaver 👏

[@FIDEL_CASHFLOW_]

Thanks for the clear and concise explanation. My teacher went over this in 45 minutes and I was more lost than when I had started looking at it. Now I can see that it's simple but just takes a fuck ton of time.

[@samiullahkhan3828]

one of the best if not THE best video made on matrices!! keep up the great content!

[@wamo693]

Wish I could thank you personally! God Bless you g

[@kaddanki096]

Shoutout to this guy for all the precalc help.

[@yangzhen2889]

Your way to resolve is more clear than text book. Thanks a lot.

[@bofelothebeemang7728]

I just go to class to note the topic and come back here.....you are a thousand times better than lectures

[@Maryam-ok6sk]

You're the absolute best! My teacher sucks but your videos help me get straight As !

[@haisal2846]

You are a Life saver and this time I ain't even lying

[@Oramosengr]

Following this video, I was able to solve my problem with different coefficients! Thank you! You have been one of my best references (tools) since 2018!

[@venom-kl3un]

Hi american , are u from Texas

[@TeddyPhiri-uc9wp]

Was told I will never understand this. But thanks it’s now simple to me

[@justiceebundomarise22]

Thanks Mr. The Organic Chemistry Tutor!!

[@africangirl6809]

I learnt this so fast, I never knew it was this easy. God bless you 😇

[@sidindian1982]

Brilliantly Explained ... Thank You Sir 🥰🥰

[@amadiroyal3910]

Your videos are very interesting and easy to understand. Thanks bro. Really.💪🏾💪🏾

[@mituberi]

you have no idea how much you eased my life thank you ,like your the best you are such a blessing i mean it , i cant thank you enough thankssssssssssss

[@abdulloh_boi]

easy, understandable, comfortable for cognition. wanna just thank you

[@Jeff-nq4hg]

All addition, subtraction, multiplication, and division, but quite a complex method. I like it!!

[@FunnyAirplaneWindow-on8sx]

Thank you so much..this video just clearify everything regarding Cramer's rule ❤

[@sababadry]

Thanks a lot you deserve all the love in the world😘😘😘

[@hasanyahya4698]

i literally watch this video for my mid term test last year and here i am right now watching the same exact video one year later for the exact same reason goddamit i failed my test :)

[@meggiefritos6630]

Bro is a lifesaver... I have a test in 1 1/2 hours and I had no clue but this makes perfect sense. Gotta love it

[@DanYansom]

I don't know why I always wanted to watch your math, Chem and physics vedio I'm always glad to watch your videos it is the best i could say i give you thums up for your time and effort

[@daviduta9187]

Thx so much man. Life saver right here

[@theodorahjanget9900]

Thank you for your time to explain such a confusing process .You have Me thinking that math is fun and it actually is so thanks.

[@karamkassem9821]

easy peasy lemon squeezy lesson, thanks so much

[@mawhadmd]

This was really Easy af, didn't expect this

[@danielteyehuago1633]

Thanks for sharing it with us

[@yourplug4850]

You're a blessing to my education !!!!!!!

[@Furapika]

your voice is like Top5S voice. So nostalgic

[@jamesheller5487]

thank you so much you explain 10x better then my College Teacher

[@djkeepton]

Am from Kenya 🇰🇪 and I really appreciate your work 🙏am now able to tackle all questions in Algebra 1,

[@ellaobi4048]

Thanks alot you are literally saving my mathematics, chemistry and physics grades every year
I really appreciate it Thanks again man

[@natashachibuye2772]

I have an exam today and I Really needed this on short notice. Thank you sm

[@yenkodelantvpuanmedia1196]

You have made math very easy and interesting 😉 thanks allot from 🇰🇪🇰🇪🇰🇪

[@zainabzaidi8634]

THANKS FOR MAKING MY LIFE EASYYYY

[@bathenkosimfihlo2380]

You're a legend 👌👍👆my role model

[@aqil475]

I was absent when my prof was teaching this, but thank god this video exists. You saved me like 5th times now 💀👍

[@spadeaxe5528]

Thank you so much!

[@ibrahimdiriye4076]

May god bless you Mr organic tutor ❤

[@quack.and.move.on.]

THIS SAVED ME. THANK YOU. May Allah bless you, alhamdulliah

[@senuri2846]

thank you so much for the help sir, you saved my life 🥺

[@truffles1]

thank you for helping, it may not mean much to you, but it means a lot to me, thank you organic chemistry tutor

[@daffo1179]

im a romanian and we do this in math in 11th grade. i wrote cramer on youtube, without anything else, showing me results in english.
checked the video, checked my notebook, realised how MUCH MORE complicated the method in this video is.

[@Animx185]

In africa we learn in grade 9

[@jadidjunan2209]

broo you're a hero,saviour

[@AndisiweNelly]

Oh man thank you so much, you are a blessing❤️❤️

[@SaraswathiSelvam-c8r]

Excellent way of explanation

[@Tokolos1]

This was very helpful. Thank you

[@nikamabaal7882]

After 8 hours I'll be in exam hall and you helped me a lot.
Thank you so much 🥰

[@funforeverything]

We love you organic chemistry tutor!!❤❤

[@kelchechim]

Thank youuu watching from Zimbabwe

[@hibuddy271]

Thank you, this was very helpful!

[@chulasawera]

Thankyou so much. You're so helpful

[@royrolls457]

if there was an award for best teacher in the world you deserve it😊😊😊

[@moonchild_9335]

This man is a life saver. Thank you so much for this lecture! 🙏

[@sharikahasan1754]

I really don't know how to thank u sir..u just saved me b4 exam..I found your channel this yr n I couldn't help commenting that U r the best...I repeat..THE BEST😢❤..

[@ShadOw-zk9nm]

Maaaaaaaaaan you're so awesome thx for the solution of this cramer exercice !

[@Kevin_Silva_]

Thank you very much! ❤

[@T8_motivation.01]

Wow that was sooo helpful 😊😊😊thanks❤👌

[@shashwat6480]

Bruhh keep up the good work , this was really helpful!

[@philipjavierocleda273]

Thank you so much for doing this video. I really appreciate it and it really help me in solving my math problems. God bless you 🙏😇🙏

[@darrenonyeoguzoro6092]

Thanks
I really needed this

[@dorcasmupeta4193]

You’re a life saver 🙌🏽