❖ Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 2 ❖

Gauss-Jordan Method - Solving Systems of Equations
In this video, we use the Gauss-Jordan method to solve a system of linear equations. By transforming the augmented matrix into reduced row-echelon form, we systematically solve for each variable. The Gauss-Jordan method is a powerful technique that provides a clear path to find solutions to systems of equations. This example helps build a strong foundation in linear algebra and shows a practical method for solving complex systems.

What You Will Learn
*) How to set up a system of linear equations as an augmented matrix
*) The step-by-step process of row operations to achieve reduced row-echelon form
*) How to interpret the final matrix to find the solution for the system
*) Tips and tricks to efficiently use the Gauss-Jordan method for solving equations

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[dkscidmore]

Been having problems with this. Never knew you could just multiple or divide a single line. That helps out a lot.

[blackenedktulu]

@patrickJMT I'm not dreading my repeat exams now. You've saved me! I literally can't thank you enough.

[Marno_YouTube]

Thank you patrickJMT for all these helpful videos. I am sure it takes a great part of your day to make all these videos? Therefore I really what to give a big thanks to you. It make my life so easier, when it test weeks.

[patrickjmt]

thanks :) although i am less concerned about that, and more concerned with giving people the tools to succeed and empower themselves and hopefully make the world a better place for all of us!

[iguanalegal]

you just saved me a big headache on my test.. thank you so much for the videos!

[ezra]

OMG THANK YOU!
:D
This literally covered something that wasn't shown from a previous video that made this whole Gauss matrix Elimination understandable!!!!
THANK YOU!!!

[geraldchristophers.espino]

Thank you Patrick, now I understand how to solve Gauss-Jordan theorem. Thanks a lot! :-)

[bsiccs]

So it's kindof like Sudoku, in which you have to just look at the rows and columns, and manipulate them to do what I want them to do...?

[musabtulaimat]

you are one of the best math teachers ever, love your stuff and wish you the best !

[SuS]

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[Elissalandon]

great videos ...
liking the way you teach ...
you are one of the person who made me like maths somehow..
simply thank you SIr

[ianchavarria.]

@patrickJMT are there times when the pattern of getting main diagonal will change?

[gamzemusluogluboylu]

thank you so so so much, Mr.Patrick! You re a life saver!

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[thomcruz]

I appreciate you taking the time to teach this formula for solving systems of equations. This is a formula that has perplexed me for over a week, and even after reading on the concept I still have not been able to wrap my mind around using the matrix as the substitution method for finding solutions. I watched your 1st example, and decided to check you work at the end to find that indeed it works. As a result I feel empowered with understanding. I get here for another example, and I feel like you move too swiftly through the problem. I realize it is because you've become a master at using the Gauss-Jordan formula, but did you ever consider that you're teaching this formula to others, it probably would've been helpful to slow down your pace and maybe explain a step here and there, so that the student can really understand why you're making these calculations. More people would probably get it a lot quicker. TJMO, I appreciate the lesson nonetheless.

[Psweezy]

dude, you Nailed this video.. Great job

[aliwacool]

It's so great learning here. Thanks a lot for the thought of placing this videos.

[hamzabinamin]

I'm getting x=82/25 y=33/25 and z=-3/5 is this correct? Can we get multiple solution for x, y and z depending on how we solved the equation?

[ankusharora]

One of the best video on this topic, Thanks a ton!

[TheFriedLife]

plss tell me why u have done 2nd element of 1st row i.e(1) zero???