Beautiful! To add to the video, the key intuition behind Gauss Jordon is as follows: We want to find the point (solution) where these three planes (rows) intersect. For that, we keep rotating (pivot) each plane along the line of intersection of two planes (rows). Since such a line always goes through the point, the point (our solution) remained unchanged as we rotate the planes in every iteration. We keep rotating them until each plane is perpendicular to an axis, at which point, the intercept at the axis reads the solution.

what an underrated channel

@sinwooyoo62

5 жыл бұрын

tell me about it. this channel just hacked my brain down and rebuilt up as with the perfect understanding. I really wanna be a patrion for this channel sincerely.

6 years later and this is still stellar content. Well done sir!

this is gold

This is gold! Fantastic! :D "Jævlig bra," as some of us say in Norwegian! This is a super clear and simple illustrative animation, and it worked incredibly well!

The geometric visual helped me make sense of the algebra. A few light bulb moments for concepts that I knew but didn't think about for this. Thank you!

Great visualization. I spent so much effort in my linear algebra class trying to visualize all this stuff, and what was happening in the transpose space. I think what would make this even better though, would be if the planes were coloured differently, and the rows of the matrix coloured matchingly, to make it easier to keep track of which planes were being added as they're being talked about. It would also be nice to see the normal vectors represented by the row entries. I think that that would make more apparent why row addition causes plane rotation.

@paulmcc8155

7 жыл бұрын

I agree that the planes should be coloured differently, rather than be merely different shades of one colour.

Amazing! A new way of understanding Gauss-Jordan Elimination.

I don't understand why linear algebra courses are so poorly designed. Most of the information that is crucial for understanding the topic is omitted from books. Do they think we are dumb and incapable of understanding such simple concepts?

So simple,relevant,intuitive and empowering. I'm starting to believe that there is a global conspiracy to keep things hard on purposem so we become more manipulable. PLEASE ADD auto-generated subs,when you accelerate videos,the normal subs lag! Thanks!!

Incredible job imparting fundamental insights & understanding! On behalf of people who don't understand it until we see it, thanks so much for helping us see it & understand!

Wow, thank you so much for this step by step with the visualization. Linear algebra is so interesting

thanks, this was actually the thing I needed to see. This adds everything up for me .... thanks again.

on a journey to improve my linear algebra and Calc 3 foundations for my machine learning major and this is an absolute beauty of a content. Keep them coming

Great visualization and prefect supplementary content regarding RREF for 3B1B's Essence of Linear Algebra!

This video is amazing! The geometric interpretation that I asked from my Linear Algebra teacher but she was unable to articulate. Please continue to make Linear Algebra, and Abstract Algebra concepts visualized in this manner. Helps build intuition and deeper understanding behind what is being done with these mathematical objects.

This helped more than u can imagine! more even then 3blue1brown, will watch the other vids as well

This is a fantastic series of lectures. Thanks a lot.

Brilliant pedagogy. Kudos.

@loden5677

11 ай бұрын

Agreed

Thank you so much for making this video.

Beautiful. This makes so much sense!

Such a great visualisation! Should have far more views

Dude, this is like magic, thanks a lot!

That's a great resource! Thank you!!

Man, this is brilliant, thanks from Czechia🇨🇿

Great content, thanks from Kazakhstan

It does an excellent job at visualizing the pivot operation.

This was a wonderful geometric interpretation , great content

This is so intuitive! Thank you

Thank you for your effort to make the video. It is great and really helpful!

best explanation of geometrical interpretation

awesome insight, but the animations are frustratingly slow. thank goodness for 1.5x speed

@MyWhyU

6 жыл бұрын

We recommend watching at whatever speed setting works best for you . Higher speeds are especially nice when viewing sections that you are already familiar with.

Beautifully done

Please keep making linear/matrix algebra videos. They are very useful for CE students like me.

really beautiful. thanks

This is awesome, thanks.

Wonderful simulation

This need WAY more love ❤️

Thanks, you rock

Thank you!

mighty brilliant

makes perfect sense

Best video❤️❤️❤️

te amamos, gracias

Very Cool

What software did you use for the animations?

I love it

MASTER!

Dude, I love you

great

Question: When we create a 3x3 (augmented, so, plus a column) matrix from a system of equations, each row of the matrix contains a possible x coordinate, a possible y coordinate, and a possible z coordinate. *However*, when I watch 3blue1brown's videos on matrix transformations, in which we interpret matrices as collections of vectors, each *column* of a 3x3 matrix contains an x component of the vector, a y component of the vector, and a z component of a vector. In other words: in this video, 1 column is x, 1 column is y, and 1 column is z. But in 3blue1brown's video about vectors in a matrix, 1 *row^is x, 1 *row* is y, and 1 *row^ is z. Why?

@ParthSharmakee

2 ай бұрын

bro i have the same question after watching 3 blue 1 brown video if each row represents x,y,z coordinates of the transformed i,j,k and vectors , then how can we subtract 2 rows as scalars . it doesnt make any sense. if you find its answer then please let me know. thanks

What software did you use to create animate the 3D plane?

@MyWhyU

Жыл бұрын

Why U typically uses "Cinema 4D" for 3D animations.

I do not know if anyone will see this in 2020. But please does anyyone have an idea of the geometrical interpretation when we have for example a system of three equations with four unknowns? Or is it that it does not have geo interpretation?

@MyWhyU

3 жыл бұрын

It would require four dimensions to create a geometrical interpretation of a system with four unknowns.

@justanotherguy469

2 жыл бұрын

@@MyWhyU As each variable represents a dimension.

🤩🤩🤩you are the bwst

Why are they a system of three planes and not a system of three vectors?

@longbowmen

3 жыл бұрын

you can view the system as the normal vectors of the planes

@valor36az

3 жыл бұрын

Because there are 3 variables in each equation. An equation of 2 variables would be represented by a vector.

@justanotherguy469

2 жыл бұрын

@@valor36az An equation of 3 variables does represent a vector, in 3 planes, the X, Y, and Z plane.

🤸🤸🤸🙅💥💃❤️🙌

like + sub . Nice explanation