[Linear Algebra] Echelon Form and Pivots

We discuss the echelon form of a matrix and what pivots are.

#LinearAlgebra #Algebra #UniversityMath #Lecture

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In this video we introduce echelon forms and pivot positions.

Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.

[pureawesomeness]

I still need more explanation about the pivots ;(

[maggielin]

Thank you for showing the pivot positions precisely in a matrix. And your voice is beautiful.

[muhammedisa]

Thank you from the bottom of my heart, I got 100 in my midterm without opening the book.

[bell]

literally the only video or notes that i finally understood what pivot means

[FatMaMohvids]

I can't thank you enough for this linear algebra videos! My final exam is tomorrow, and I've gone through the whole course without understanding anything at all, somehow I stubbed upon your channel and Oh My God I've never been so thankful in my life❤️❤️❤️ thank you! To the edge of the universe and back!

[pineapplesharm]

Thank you so much for your explanation. This definitely helped quite a lot to clarify row echelon and reduced row echelon form.

[ahmedaathif]

Thz for explaining well !! I understood the concepts!!

[luckyjan]

Tq after watching many videos i got to know frm ur channel

[mohammadjibawi]

does it matter if you switched the second and the third rows to your final answer? (I'm talking about the last example)

[Ppooh]

At 1:36 shouldn't it be diagonal whete the pivot would be 3rd in row 3?

[doruktopcu]

Thank you very much for the examples. But I feel like I need to find more examples for ref problems. Where can I find em?

[lippy]

Hi, what app are you using to write all these things? eg. the black board with all the different marker colours. It's so convenient, i want to download it too :)

[MrEdstorm]

If the zeros must be on the bottom row, why in the second example can a number be on the bottom row last column. Just a bit confused

[horikatanifuji]

shouldn't the pivot positions be the x2 on the 3rd row and the x3 on the 2nd row because you had to swap your row2 and row3 to get your reduced echelon form? Just a genuine question since I'm currently learning this in class.

[danielbreen]

Did you mean to say augmented "column" rather than "row"? Serious question. I haven't learned it all yet, so it's hard to know if an augmented row is something I haven't learned about yet or not.

[ohmymahone]

isn't the last matrix in row reduced echelon form? on 7:22

[I_am_root]

r2 and r3 are changed but the pivot positions are still there?

[ThePikmania]

Thanks for your tutorials Trev, they help me a lot. :)

You just missed a subtle but important detail at 2:10 at requirement 5). There CAN BE entries in a column besides 1 or 0 IFF the column is not a column with a leading 1.

A more precise definition from Wikipedia would be: "Each column containing a leading 1 has zeros everywhere else"

[markchaniotis]

Why don't we just do :R1+R2 for the first row and then the same for Row 2? (by 8:30)