Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra

then in this case what would be the vector B representing when AX=B has infinite solution , if only one solution it implies that B is in the span of the column vectors of A .what would be B if no. of solution is infinite , so if A is 3*2 then would it mean that B is the entire span(plane)

Sir your work is Art.

this series is genius

love it, vivid

Math ASMR.

Bravo! Way to go - great visuals! Without them students are lost. Thank you!

Thank you so much !!!!!!!

each coordinate is a real combination of numbers of a base right? It could be (pi, sqrt(2)). This is ok?

A fun little application of span: a simple way to render simplistic 3D graphics (I don't think this is used in the video) is to place i, j, and k somewhere on your 2D screen. Their span is 2D, so the entire 3D scene is now on the 2D plane. This is called orthographic projection. Obviously the rendering process is a little more complicated and most renderers don't do this.

انت مثل القمر تضيء ، ولاتنتظر ان يشكرك احد ، وتستحق الشكر ، شكرا لك.

Are these the same concepts people use for visualising large mental arithmetic?

Great explanation, thank you.

Is it the case that, for every integer "n", the number of possible ordered sequences of "n" digits is smaller than the number of possible chaotic sequences of "n" digits?
For instance: is it true that for every possible sequence of 4 digits, there are less sequences like 2-2-2-2, 1-2-3-4, and 2-6-2-6 (ordered) than sequences like 1-7-3-9, 3-3-0-1 and 5-7-2-7 (chaotic)?

Amazing explanation. I’m a math major and this video makes the gibberish in the book a lot more understandable. Thank you

love you, graham

I recently attended a linear algebra exam which in spite I worked it out, now I wish I found this video before it would've saved me a lot of time just delving into the bulky text book to understand those concepts

wonderful

I will remember the concept for life!!!

that conclusion was mind blowing

thankyou

I used to feel that I'm in some kind of existential crisis whenever I try to learn linear algebra but these videos making sense why we are using linear algebra.
Thanks a lot mr.grant sanderson

I feel smarter now

Bro This series are littrarly a whole semester from my college in 1 hour!

jesus christ THATS what you mean by linearly dependent

Appreciate the knowledge

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I suddenly realized that my country's education is the wrong approach

Omg so amazing animation💝

Hey!. Thank you very much, for this nice video. Let me ask you a question: ¿What music did you use at the end of this video?

THANKYOU

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I have just learned about vector both in physics and computer science but no one could explain as clear and understandable as you. I love this playlist "Essence of linear algebra" and every video you make. Hope you will get more subscribers, I will share this channel to my friends.

Amazing video❤

So good lecture. In linear combination, when you say that fixed one scaler, then move another, I think the result vector is not a line, but a rectangle region

instead of mechanically calculating i finally understand what they actually mean thank you for the videos

I sincerely hope you are being paid for this.

Amazing！

This is confusing it is not for me 😭

번역이 최악이라 뭐라는지 계속 정지해서 자막 읽고 고민해야함 ㅡㅡ;;

Hey your videos are more clear and more interesting that any complete undergraduate course about linear algebra!

Lucky to be born in this era ❤

I think you should get a prize for these videos!
I can only thank you for it now, wish I had it when I started mechanical engineer years ago.

This is poetry. All your videos are master works and go a long way in shaping how one should think about mathematics, visualising hard concepts, and their relevance in solving real world challenges. Thank you for your incredible contribution.

i come from fujian of china,u made amazing animation aboat vector. i have calculus understanding,but linear algebra is much difficult,need a lot imagination。thank you,good man.

Bro I don't know why nothing is just making sense

This is like Visual Gilbert Strang !!

Can anyone tell me if this play list is Everything we will learn in cegep when they say linear algebra