Solving a 3x3 System Using Cramer's Rule (Example)

This video steps through how to solve a linear system in 3 variables using Cramer's Rule. It focuses on manipulating the coefficient matrix and evaluating determinants to solve for each of the variables.
For more math help and resources, visit www.hsmathsolutions.com.

Пікірлер: 107

  • @bigmt1986
    @bigmt19863 жыл бұрын

    Cramer's rule aside, your handwriting is what I want to learn.

  • @levi_exiled8579

    @levi_exiled8579

    3 жыл бұрын

    yep.

  • @Opportunist1

    @Opportunist1

    2 жыл бұрын

    Yes brother

  • @ventousemoustachue
    @ventousemoustachue3 жыл бұрын

    I used to do Adjugate Matrix/Cofactor Matrix and Transformation Matrix and mix them up to get something that takes longer to do than using the normal way to solve these without matrixes. But then you show me this that is super intuitive and super simple

  • @ryanmeister4431
    @ryanmeister4431 Жыл бұрын

    Great video James! I've been exploring a more efficient way to solve for 3 variables via Cramer's Rule: After finding 2 of the unknowns, plug them back into one of the original equations. Solve for the third variable. Plug all three variables into the equations to check your work. I hope someone finds this "quick and dirty" method helpful!

  • @reedbrett5252
    @reedbrett52524 жыл бұрын

    Why did I never learn this in school. a lot easier in some cases.

  • @patrishanotpatricia6456
    @patrishanotpatricia64564 жыл бұрын

    Couldn’t explain it better. So awesome thanks!!!!

  • @kaysidegamer5996
    @kaysidegamer59964 жыл бұрын

    super useful and uber concise, thank you!

  • @prashantthakur23
    @prashantthakur233 жыл бұрын

    Hyy sir I am from india nd prepare for iit It's great method to solve Thanks lot to give clear technique.... 🥰

  • @robertp2934
    @robertp29349 ай бұрын

    Awesome simple, step by step explanation. Plugging in the values x, y, z and the equations are proven!! (1/2, -2/3, 5/6). Revisiting my love for mathematics. Thank you, Sir

  • @JorgeLopez-tx1dt
    @JorgeLopez-tx1dt5 жыл бұрын

    Thanks for making this video. It really helped me out.

  • @rahulkota2393

    @rahulkota2393

    4 жыл бұрын

    Ok

  • @corneliussmith5938
    @corneliussmith59382 жыл бұрын

    Beyond helpful. This is by far the most simple and efficient way to solve systems of equations. Thank you!

  • @justachildofGod
    @justachildofGod Жыл бұрын

    Just wanted to say your handwriting is the neatest most beautiful print i have ever seen

  • @lololologan
    @lololologan4 жыл бұрын

    Wow easy to understand !!!! Thank you!

  • @matildahmatyolo2153
    @matildahmatyolo2153 Жыл бұрын

    Wow this is straightforward... Thank you

  • @supergreenkimmayong5488
    @supergreenkimmayong54883 жыл бұрын

    This fast solution is what I'm looking for.

  • @Austindragonrider
    @Austindragonrider4 жыл бұрын

    bro thanks so much my professor makes everything so complicated

  • @kessjenner8895
    @kessjenner88954 жыл бұрын

    Wow this is an easy method of linear system than equation by elimination prone to errors. Btw tnx man you did great just keep uploading math videos so very helpful

  • @teacherche8757

    @teacherche8757

    4 жыл бұрын

    kess jenner elimination is better

  • @JBuck1935

    @JBuck1935

    Жыл бұрын

    Oh, trust me. There is still plenty of room for errors in this method, too. But I understand the process much better now than I ever have.

  • @huskygt380
    @huskygt3802 жыл бұрын

    this is exactly what i needed

  • @LeFARaJ
    @LeFARaJ4 жыл бұрын

    great video mate , thanks alot .

  • @kudakwasheprincechidakwa8798
    @kudakwasheprincechidakwa87984 жыл бұрын

    you're legit bro!!!!

  • @ashma101
    @ashma1013 жыл бұрын

    Thank you so much for the explanation. Greetings from Indonesia

  • @hsmathsolutions

    @hsmathsolutions

    3 жыл бұрын

    You are most welcome!

  • @dawnguardiano7216
    @dawnguardiano72163 жыл бұрын

    THANK YOU VERY MUCH!

  • @mitreshravi3552
    @mitreshravi35522 жыл бұрын

    Thank you sir for helping me understand Cramer's rule...

  • @JBuck1935

    @JBuck1935

    Жыл бұрын

    This video is the only one I've found that makes it crystal clear what the algorithm is to solve these. This is good, because I'm taking a very significant math test next week for an endorsement for middle school math. 5 hours long. OOOOoooooofffffff. Not really looking forward to this!

  • @erikmartinez6726
    @erikmartinez6726 Жыл бұрын

    Thank so much! This really helped! God bless!

  • @velipslii3772
    @velipslii37728 ай бұрын

    Thnx a lot man you really helped me

  • @SipDahara
    @SipDahara3 жыл бұрын

    it' s great method .. Thanks a lot..

  • @vinayajoseph7025
    @vinayajoseph70252 жыл бұрын

    Thank you for the video.

  • @baharehghafari1454
    @baharehghafari14544 жыл бұрын

    Thanks. It's the best.

  • @mathematicscollection6370
    @mathematicscollection63703 жыл бұрын

    Nice Explanation Good method

  • @harismalik6601
    @harismalik66013 жыл бұрын

    thanks mate for a great video

  • @hsmathsolutions

    @hsmathsolutions

    3 жыл бұрын

    You’re welcome!

  • @ushakalyanijetti4988
    @ushakalyanijetti4988 Жыл бұрын

    It's very too short and simple tq ☺️

  • @sahadhura8927
    @sahadhura89273 жыл бұрын

    Thanks sir i didn't get anything in class but understood every bit of this crammer rule in your class

  • @hsmathsolutions

    @hsmathsolutions

    3 жыл бұрын

    Great! I'm glad I could help!

  • @sahadhura8927

    @sahadhura8927

    3 жыл бұрын

    @@hsmathsolutions sir where r u from

  • @YounisKhan970v
    @YounisKhan970v4 жыл бұрын

    Thank you !

  • @Klayx_
    @Klayx_2 жыл бұрын

    very good explanation thank you

  • @maramalzayer6614
    @maramalzayer66144 жыл бұрын

    it made everything clear

  • @economicswithsajid
    @economicswithsajid3 жыл бұрын

    Great sr ❤️

  • @chishangoma9676
    @chishangoma96764 жыл бұрын

    thanks so much.

  • @jayfegade3595
    @jayfegade35954 жыл бұрын

    Thanks 🙏🏻

  • @astroboy5040
    @astroboy50403 жыл бұрын

    Thank you so much sir .... It helped me alot

  • @hsmathsolutions

    @hsmathsolutions

    3 жыл бұрын

    You’re very welcome!

  • @montealadadi3088
    @montealadadi3088 Жыл бұрын

    Thank you

  • @ProfessorBlue
    @ProfessorBlue4 жыл бұрын

    thx man it hleped me alot not like dum teacher tech hech and said the answer is wrong but the steps are right but he confuse by 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000% thx man your the best 👌 peace bro have great life and be good and have fun 24/7

  • @grimmmaster7189
    @grimmmaster71893 жыл бұрын

    Nice work

  • @kimjibilliondegreedragon7073
    @kimjibilliondegreedragon70734 жыл бұрын

    Thanks master

  • @hamiltonfungula63
    @hamiltonfungula633 жыл бұрын

    Few hours b4 exams I am here I understood it, now am off to kill the paper...Thank u Sr.

  • @fareskhoja8825
    @fareskhoja8825 Жыл бұрын

    very helpful

  • @JamezBnd007
    @JamezBnd0074 жыл бұрын

    life saverrrrrrrrrrrrr!!!!!!!

  • @rahulkota2393
    @rahulkota23934 жыл бұрын

    Thanks

  • @215Tate
    @215Tate Жыл бұрын

    Thx man

  • @DutchKing
    @DutchKing4 жыл бұрын

    You are a god.

  • @kiranrandhawa6120
    @kiranrandhawa61204 жыл бұрын

    helpful video

  • @jakeugyu6711
    @jakeugyu67114 жыл бұрын

    Very understand

  • @pidepiper5693
    @pidepiper56933 жыл бұрын

    Thank you so much

  • @hsmathsolutions

    @hsmathsolutions

    3 жыл бұрын

    You're most welcome!

  • @ammarah_3092
    @ammarah_30923 жыл бұрын

    thankuu sooo much, it really helped mee ^_^

  • @anij7898
    @anij78984 жыл бұрын

    Thank you for this video! Does anyone know what pen that is ??!!

  • @hsmathsolutions

    @hsmathsolutions

    4 жыл бұрын

    Anisah J -Pilot G2 .07

  • @anij7898

    @anij7898

    4 жыл бұрын

    @@hsmathsolutions Thank you !

  • @robertp2934
    @robertp29349 ай бұрын

    Hello James. What musical instruments do you play? I am a woodwind enthusiast.

  • @amalalhosani2334
    @amalalhosani23343 жыл бұрын

    Thxxxx alooot

  • @ccchua6982
    @ccchua69824 жыл бұрын

    lt easy to understand

  • @kudakwasheprincechidakwa8798

    @kudakwasheprincechidakwa8798

    4 жыл бұрын

    4real

  • @sqmps8709
    @sqmps8709 Жыл бұрын

    God bless you

  • @user-fe6mn6is5s
    @user-fe6mn6is5s7 ай бұрын

    How do you solve x-2y + z=-1 3x - 2y -2z=7 x + 3y-2z = 5 Using crammers rule

  • @madrazodarryll4787
    @madrazodarryll47873 жыл бұрын

    Only -15 will be touched by negative?

  • @adabatool6721
    @adabatool67213 жыл бұрын

    That handwriting is my handwriting dream

  • @AR-vb4xy
    @AR-vb4xy3 жыл бұрын

    Basically he is using Cramer's rule and Sarrus's rule. The method he is using seems like a neat alternative for converting the coefficient matrix augmented with the constant matrix and converting it to row echelon or Reduced row echelon form.

  • @munditistany5618
    @munditistany56186 ай бұрын

  • @belgirevaldo1924
    @belgirevaldo19244 жыл бұрын

    done

  • @alexandrospanag
    @alexandrospanag3 жыл бұрын

    your method was actually really harder than what it actually is... using a finger while looking at the row (up+down) and seeing the rest of the values is way easier 100%

  • @saniamadarbccus4351
    @saniamadarbccus43514 жыл бұрын

    Can this method be used for a 4x4 matrix?

  • @hsmathsolutions

    @hsmathsolutions

    4 жыл бұрын

    Sania Madarbccus Yes. The beauty of Cramer’s Rule is in its simplicity and ability to extend over any size system.

  • @saniamadarbccus4351

    @saniamadarbccus4351

    4 жыл бұрын

    James Elliott thank you so much...

  • @bikrambhatt

    @bikrambhatt

    4 жыл бұрын

    @@hsmathsolutions , Can you please make a video on how to extend this approach for any size of matrix including 4X4

  • @supergreenkimmayong5488
    @supergreenkimmayong54883 жыл бұрын

    Can you do a 4x4?

  • @hsmathsolutions

    @hsmathsolutions

    3 жыл бұрын

    Yup! You can do any size system. Just follow the same procedure, but extend it for 4x4 (4 variables). The problem is that finding determinants for larger square matrices can be quite a challenge (lots of busy numeric computations). It's often better left for a computer system!

  • @supergreenkimmayong5488

    @supergreenkimmayong5488

    3 жыл бұрын

    @@hsmathsolutions Thank you. It would be great and really helpful to know how you'd solve a 4x4 with Cramer's since I couldn't find any example with your method.

  • @simonkibera4722
    @simonkibera4722 Жыл бұрын

    The determinant is 27; and y=-11 so I doubt the answers

  • @cherrycris7568
    @cherrycris75683 жыл бұрын

    Hope no text in screen

  • @doreenkennedy8163
    @doreenkennedy81633 жыл бұрын

    Hey babe I like your handwriting aaaw😛😍

  • @luckytravelerofficial
    @luckytravelerofficial4 жыл бұрын

    Its so hard

  • @tiaan8551
    @tiaan85512 жыл бұрын

    bruh why didnt my teacher tech my the diagonal method

  • @livhuwaninenngwekhulu6508
    @livhuwaninenngwekhulu65082 жыл бұрын

    Your answers are wrong man when I prove they don't give me the original answers from the equation why...??

  • @livhuwaninenngwekhulu6508
    @livhuwaninenngwekhulu65082 жыл бұрын

    Ow sorry I left a negative sign

  • @shresthanisan2
    @shresthanisan22 жыл бұрын

    This is SARRUS rule.😅

  • @javedkhan-hk2vn
    @javedkhan-hk2vn3 жыл бұрын

    this method does not work on all linear equation sorry Bro.

  • @hsmathsolutions

    @hsmathsolutions

    3 жыл бұрын

    Cramer's Rule is ubiquitous. It works for every linear system. This video covers linear systems that have single ordered triplet solutions. Cramer's Rule also covers systems with no solution and infinite solutions, but not in this video.

  • @theodosissarmadakis913
    @theodosissarmadakis9134 жыл бұрын

    why tf you find the determinant this way? its stupid

  • @patrishanotpatricia6456

    @patrishanotpatricia6456

    4 жыл бұрын

    Explain it your way then

  • @malekbiar3832

    @malekbiar3832

    4 жыл бұрын

    Wow thanks.

  • @theodosissarmadakis913

    @theodosissarmadakis913

    4 жыл бұрын

    @@patrishanotpatricia6456 you take the first item of the first row and multiply it by the determinant that its left if you remove the row and column that the item is in to then add (-the 2nd item on 1st row)* the determinant of the array without the 1st row and 2nd column then add (+3rd item on 1st row) and it goes on like this for all the items in the first row going(+,-,+,-...)and this way its just a polyonym

  • @mamadetaslimtorabally7363

    @mamadetaslimtorabally7363

    4 жыл бұрын

    It's because it is a valid method approved by any examining board idiot!!!

  • @rickyvarquez5955
    @rickyvarquez59552 жыл бұрын

    I don't understand anything 😂

  • @MATRIXz
    @MATRIXz2 жыл бұрын

    Thanks

  • @chandrasensingh3459
    @chandrasensingh34594 жыл бұрын

    Thanks