How to Find the Pivots and Pivot Columns of a Matrix From Row Echelon Form

In this video I will take you through a step by step tutorial I will show you how to put a matrix into row echelon form using elementary matrix operations (i.e. Gaussian elimination/row operations) to find what the pivots of a matrix are and to identify the pivot columns of a matrix. This video tries to explain simply what row echelon form is, the staircase pattern and the identification of pivots.

It is also worth knowing that the number of pivots is equal to the rank of a matrix

[peterlinhan]

This video is the clearest and the most easy explanation and the clearest English pronunciation.

[isaacvrba]

I'm taking a Matrices and Linear Algebra class right now and you just explained to me something in a fraction of the time my prof did and I still didn't understand everything they were trying to say. Thanks a lot!

[ammishaddaiasafoagyei]

I was so confused, you just made my day. So much precise explanation to make it very understandable. Thanks much

[vsalinas]

Thank you for your wonderfully clear videos. They are extremely helpful, and have helped me to learn so much!

[de_vics]

Thank you so much! YouTube teachers are the best for real!

[nazziwasarah]

Am glad I have learnt something. Thank u

[lekien]

i was so confused until i watched ur video, thank you for enlighten me!

[easytube]

Thank you. You made it easy to understand...

[Winchester_]

Omg thanx so much haha

In the linear algebra lectures I wasn't able to understand why not every column was a pivot column if it had a non-zero entry; now I do!

[iron_zeppelin]

Thank you, you explained this concept much more clearly and concisely than my textbook did.

[jacoblinnarsson]

Super helpful, very good explanation! My professor didn't even tell us what Pivots are and just told us to read our book. Doesn't help that the book is in English which isn't even my first language. Thanks for your help!

[RubiMercuri]

You explained this perfectly thankyou!

[devyanshagrawal]

In the last example you showed, the last row didn’t have all zeroes at the bottom ( 0 0 4). But you had mentioned one of the rules to have a row echelon form is to have the last row as all zeroes. I was a bit confused by this, could you provide some clarity ?
Thanks

[archerdev]

Great lecture, thanks.
A stupid question I have, so is it possible to find position of pivot n, while matrix is in REF, but with some row exchanged?
for instance, let
A=[
1 2 3
0 0 7
0 5 1 ]
In above, rows 2 and 3 must be exchanged, but can we tell 2nd pivot is 7 in A?

[marcobocari]

5th video and finally i understand. Thank you

[fyrerayne]

Same rules for determining if augmented columns are pivot columns?

[pencilcat]

I think I've just been saved! Thanks a ton <3

[niccolomurtas]

Sir, your lesson was wonderful and clear. A plus is your English pronunciation which makes it seem to a non-english that Boris Johnson is explaining math homework to his richy, little, offspring.

[ombhansali]

is it mandatory to have all zeros in the last row in the row echelon form

[stefanijacunska]

Shouldn't all leading enteries of each row be 1? Thants what I saw in a different video