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.

[@bigmt1986]

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

[@levi_exiled8579]

yep.

[@VICTORY_5]

Yes brother

[@ventousemoustachue]

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]

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!

[@robertp2934]

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

[@corneliussmith5938]

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

[@prashantthakur23]

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

[@justachildofGod]

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

[@JorgeLopez-tx1dt]

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

[@rahulkota2393]

Ok

[@reedbrett5252]

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

[@patrishanotpatricia6456]

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

[@kessjenner8895]

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]

kess jenner elimination is better

[@JBuck1935]

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.

[@matildahmatyolo2153]

Wow this is straightforward... Thank you

[@mitreshravi3552]

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

[@JBuck1935]

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!

[@sahadhura8927]

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

[@hsmathsolutions]

Great! I'm glad I could help!

[@sahadhura8927]

@@hsmathsolutions sir where r u from

[@kaysidegamer5996]

super useful and uber concise, thank you!

[@supergreenkimmayong5488]

This fast solution is what I'm looking for.

[@ashma101]

Thank you so much for the explanation. Greetings from Indonesia

[@hsmathsolutions]

You are most welcome!

[@huskygt380]

this is exactly what i needed

[@robertp2934]

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

[@ushakalyanijetti4988]

It's very too short and simple tq ☺️

[@velipslii3772]

Thnx a lot man you really helped me

[@mathematicscollection6370]

Nice Explanation Good method

[@erikmartinez6726]

Thank so much! This really helped! God bless!

[@vinayajoseph7025]

Thank you for the video.

[@dawnguardiano7216]

THANK YOU VERY MUCH!

[@SipDahara]

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

[@hamiltonfungula63]

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

[@anij7898]

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

[@hsmathsolutions]

Anisah J -Pilot G2 .07

[@anij7898]

@@hsmathsolutions Thank you !

[@lololologan]

Wow easy to understand !!!! Thank you!

[@harismalik6601]

thanks mate for a great video

[@hsmathsolutions]

You’re welcome!

[@Klayx_]

very good explanation thank you

[@kudakwasheprincechidakwa8798]

you're legit bro!!!!

[@astroboy5040]

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

[@hsmathsolutions]

You’re very welcome!

[@LeFARaJ]

great video mate , thanks alot .

[@montealadadi3088]

Thank you

[@fareskhoja8825]

very helpful

[@grimmmaster7189]

Nice work

[@rahulkota2393]

Thanks

[@AR-vb4xy]

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.

[@economicswithsajid]

Great sr ❤️

[@madrazodarryll4787]

Only -15 will be touched by negative?

[@YounisKhan970v]

Thank you !

[@baharehghafari1454]

Thanks. It's the best.

[@BonjeVelemu]

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

[@pidepiper5693]

Thank you so much

[@hsmathsolutions]

You're most welcome!

[@ProfessorBlue]

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

[@maramalzayer6614]

it made everything clear

[@sqmps8709]

God bless you

[@chishangoma9676]

thanks so much.

[@adabatool6721]

That handwriting is my handwriting dream

[@215Tate]

Thx man

[@JamezBnd007]

life saverrrrrrrrrrrrr!!!!!!!

[@ccchua6982]

lt easy to understand

[@kudakwasheprincechidakwa8798]

4real

[@alexandrospanag]

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%

[@jayfegade3595]

Thanks 🙏🏻

[@Shehzadimtiyazbros]

helpful video

[@kimjibilliondegreedragon7073]

Thanks master

[@DutchKing]

You are a god.

[@saniamadarbccus4351]

Can this method be used for a 4x4 matrix?

[@hsmathsolutions]

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

[@saniamadarbccus4351]

James Elliott thank you so much...

[@bikrambhatt]

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

[@jakeugyu6711]

Very understand

[@ammarah_3092]

thankuu sooo much, it really helped mee ^_^

[@amalalhosani2334]

Thxxxx alooot

[@simonkibera4722]

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

[@supergreenkimmayong5488]

Can you do a 4x4?

[@hsmathsolutions]

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]

@@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.

[@munditistany5618]

❤

[@livhuwaninenngwekhulu6508]

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

[@cherrycris7568]

Hope no text in screen

[@doreenkennedy8163]

Hey babe I like your handwriting aaaw😛😍

[@tiaan8551]

bruh why didnt my teacher tech my the diagonal method

[@belgirevaldo1924]

done

[@livhuwaninenngwekhulu6508]

Ow sorry I left a negative sign

[@shresthanisan2]

This is SARRUS rule.😅

[@javedkhan-hk2vn]

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

[@hsmathsolutions]

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.

[@luckytravelerofficial]

Its so hard

[@rickyvarquez5955]

I don't understand anything 😂

[@theodosissarmadakis913]

why tf you find the determinant this way? its stupid

[@patrishanotpatricia6456]

Explain it your way then

[@malekbiar3832]

Wow thanks.

[@theodosissarmadakis913]

@@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]

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

[@MATRIXz]

Thanks

[@chandrasensingh3459]

Thanks