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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[@kraig800i]

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

[@benp2320]

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!

[@michaelfriedman2192]

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!

[@MathHacks]

You’re welcome! Best wishes with all your maths!! 😊

[@TracyR4]

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.

[@MathHacks]

Great question! Yes you can definitely use Cramer’s rule for this type of problem as well. The benefit of using Gaussian elimination is that it remains roughly the same amount of steps when you go about solving larger matrices, whereas to use cramers rule for larger matrices you end up having to do more and more work as the system gets bigger. But cramers rule is another great approach to solving 3 variable systems / 3x3 matrices!!

[@anthonylorenti945]

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.

[@ianbobby3853]

simp

[@Tapintherap7238]

So you can’t subtract rows ?

[@Jpbrennecke]

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

[@MathHacks]

You betcha! 🙂

[@astreroid118]

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

[@buhlembelani856]

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

[@mangolighttt]

Omg you just saved my Algebra grade thank youuu:)

[@MathHacks]

Yay! 🙌🏼

[@Tapintherap7238]

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

[@abdulmujibahmad3276]

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

[@ronmarkparagile5377]

I love youuu

[@buzzz241]

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

[@ryanmacewen511]

Two Step 2's?

[@bumblebiscuit5040]

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

[@math_plus4052]

Thankx

[@rrbar14]

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

[@boburmurtozaev2614]

Are there gonna be more Linear Algebra topics?

[@pathofnoor3705]

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.

[@MathHacks]

Thank you! I just started the channel a few months ago, so I’m hoping that with time the word will spread! Thank you for watching ♥️

[@DarkGharren]

Amazing!

[@yung-bbreezy1773]

I love your video, really helped thank you so much

[@MathHacks]

You’re welcome! I’m so glad it helped you!

[@shinealimec]

Thank you for this! :)

[@MathHacks]

You’re welcome! 😊