Solve 3x3 systems with matrices (Gaussian elimination - row reduction) | Math Hacks

In this introductory Linear Algebra tutorial, Brett shows you how to solve a 3x3 system of equations with three variables using Gaussian Elimination also known as row reduction. You'll learn how to transcribe a system of equations into an augmented matrix as well as the rules you can apply to the augmented matrix to manipulate it into both row echelon (also known as triangular form) and reduced row echelon form. In the end, you will easily be able to read off the solution, aka the intersection point of the three planes, from the matrix.

The THREE RULES you can use to row reduce your matrix are:
1. You can swap any two rows
2. You can multiply any row by a constant (including positive, negative, and fractional numbers)
3. You can add any two rows together

*Remember you can combine the rules together in any row reduction, as needed :)

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[benp]

I'm gonna cry. I spent 2 hours watching several videos on this topic and I still could not understand them until I watched yours. Thank you so so much for this explanation!

[anthonylorenti]

Brett, if I were your evaluator ... you would earn an A+ from me. Great teaching on all levels -- personality, enthusiasm, clarity, task analysis ... you did it all ... and you did it spectacularly well. Standing ovation from me a retired mentor teacher.

[michaelfriedman]

I was having difficulties following this transition at the LA course from Imperial College of London (Coursera). This explanation is much more clear and now I feel confident with the LA. Will continue with this site for LA and beyond. Thanks!

[buhlembelani]

Thank you so much for making it easier I'm so glad I came across your channel

[kraigi]

....and like magic I was suddenly in High School trying to understand what was the shape of a banana

[buzzz]

Beautiful! Clear & Concise! Very legible handwriting with clear visuals & explanations! 😊 Thank you!

[astreroid]

Thank you so much for this video. I was having a lot of trouble understanding until you explained it.

[Jpbrennecke]

Love it! More matrix/linalg stuff please!! I could really use it!

[bumblebiscuit]

thanks for making an organized video with rules, principles, and instructions of 'why'. so many other videos only walk through the steps without explaining the goal

[TracyR]

Thank you for sharing this video. It has helped me understand Gussian elimination better. What is the difference between using this and Cramer's rule? This seems like a lot of work in comparrison.

[mangolighttt]

Omg you just saved my Algebra grade thank youuu:)

[rrbar]

Came across this randomly but glad I clicked on it! I will be taking a class soon that has a section on linear algebra and it will be super helpful to know this going into it

[pathofnoor]

Hello Brett. I'm from Bangladesh and I found this channel by browsing Infinite Hotel Room Paradox in Medium. I really love the way you explain but Im surprised to see that you dont have much viewers even though you put an insane amount of effort. I hope your channel grows fast.

[ismaeltapia]

Will the same method of steps get the right answer every time ?

[yung-bbreezy]

I love your video, really helped thank you so much

[boburmurtozaev]

Are there gonna be more Linear Algebra topics?

[abdulmujibahmad]

Hi lodi.... your my lods...HAHAHAHAHA