Elementary Linear Algebra: Echelon Form of a Matrix, Part 3

In this video we describe how to use echelon forms to describe the solution set of a linear system of equations. This is the third video in a 3-part series.

[dokyungsoo]

It’s been 10 years but still working out wow it’s legend

[mdmushfiqulislam]

Really grateful to you.You have explained something in less than 30 minute what my Math teacher tried to explain more than 3 class(1 class=50 minute)

[rohanislam]

I see many videos for solving system of linear equation....but your videos are more helpful for me

[dipeshkarki]

one of the clear and best video of echelon form on YouTube

[HamblinMath]

Echelon form tells you which columns are pivot columns. If the system is consistent (i.e., the last column of the augmented matrix is not a pivot column) and you have a non-pivot column other than the last column, then the system has infinitely many solutions. If the system is consistent, but all of the columns of the augmented matrix (other than the last column) are pivot columns, then there is a unique solution.

[mcoban]

It is clear tutorial, thanks for your tutorial James. Appreciate!

[HamblinMath]

Good catch! I fixed it, thanks for letting me know.

[tolearnjava]

great video. Shame your channel did not pick up. you are great

[AsmaaFaris]

I can't thank you enough; I've never understood matrix and row operations before, but now I finally got the hang of it! I wish you were my math professor, haha. Thanks!

[pinface]

almost 10 years later, thanks for the lesson

[joncolumbino]

Really good explanation and variables made it super easy to understand thank you for this

[MrAshish]

i understand that using echelon form we can tell that either system is consistent or not, but if its consistent than how we can tell that that it has finite or infinite solutions just by using echelon matrix and not rref ? I want to refer to end of video at 8:16

[jsurinderveygal]

Thank You, Thank You very very much. 3 lectures and I could not get it until now. Thank you so very much.

[Ahmed-tyfd]

Thank you sir!
Explained it in the easiest possible way!

[okaner]

beautifully explained, simplified with good examples.Thank you very much.

[jacquelineecheverria-rouss]

This was the best video out there!! Amazing series :)

[michaelandersen]

Do you happen to still have the slideshow? I am attending an exam where computers aren't allowed, but if i could print this and bring it, it would be of much help! :-)

[Texxyify]

Your link is broken in part 2 to this video.