Matrices to solve a vector combination problem

stickymage Says:

Sep 28, 2009 - I agree that he needs to "draw what he mentions". What I disagree on is making us watch him draw a Cartesian plane, label the axis, switch colors, etc etc. These are periods where we are not learning anything, he usually doesn't even talk much while he is busy setting up the picture. I usually find myself skipping ahead +30 seconds just so I can get back to actual problem solving.

crapManDos Says:

Oct 14, 2009 - enjoyed learning.. thanks..

zinizterz Says:

Oct 18, 2009 - To the people saying that he needs to skip the Cartesian plane and stuff. These videos are meant to be for learners. The whole point of the you tube video, is that you can skip ahead if you think its not necessary, and you can replay it if you've missed something. Consider if the person didn't know how to draw a cartesian plane? I know you might say "He should learn that first", but including it here doesn't lose anything really.

alankarmisra Says:

Oct 20, 2009 - I'm a visual learner. Watching him draw, watching him think on his drawing board and watching him "clean up" his drawings are a substantial source of learning for me at the intuitive level. Even if he's drawing something he's drawn a 100 times in previous videos, it only adds to my comfort level with the subject. I guess he is trying to keep the videos as detailed as possible, so people like me don't lose out and people like you can skip ahead. That way the same video caters to most if not all.

Amanuel3020 Says:

Nov 15, 2009 - which one is the previous video to this one?

DanielDane9SecondAcc Says:

Nov 22, 2009 - Check his website.

tomernd1 Says:

Dec 18, 2009 - Hi, can anyone help me?I understand that the b vector is the linear combination of the 2 first vectors.I also understand that its the same problem as solving the x,y equation, but what I fail to understand is why *intuitively* we can multiply the first scalar of first vector by x and the second scalar of the second vector by y to get the b, i mean it looks like we are mixing up x,y

cvd316316 Says:

Dec 22, 2009 - That is the point tomernd1. Isn't a coordinate represented by (x,y)? Your idea of 2D (x,y) coordinates have a definite connection to all of linear algebra.

developero09 Says:

Mar 23, 2010 - Thank you for all the lessons. Nice Paint drawing too, especially humat hands with pointing fingers.Combination of fingers with predominant middle finger :)

dez3192 Says:

May 26, 2010 - leap of faith, ahaha moment, love this guy

Stencil25 Says:

Jun 16, 2010 - 8:30 Why not solve simultaniously?

csarikaya Says:

Jun 23, 2010 - Khan please stop apologising when you go in to detail. You are a great instructor.

Oh4Chrissake Says:

Jul 23, 2010 - Sal is my hero.

budman533 Says:

Dec 21, 2010 - 12:30 is the best part

tomasiscool Says:

Dec 31, 2010 - What applications would the mentioned "vector space" have? It seems like it'd be most useful in n-dimensional analysis, but I can't understand its value for vector calculus. Does anyone know what it's for? Topology?

kvn89 Says:

Jan 31, 2011 - cant you just put it right into the augmented matrix?

supakitten Says:

May 18, 2011 - isn't it suppose to be -12??cuz -6x2=-12

juaneco1980 Says:

Jun 6, 2011 - I think he's we're supposed to take for granted that matrix multiplication is associative right? Otherwise this wouldn't work since he's pretty much doing this: (A inverse)* ( (A) * (x) ) = ( (A inverse) * (A) ) * (x) , but how do we know that's true? Am I missing something or did everyone else did instead? I just googled it and I know matrix multiplication IS associative but can't understand the proof :(

KAYAKMAHN Says:

Aug 29, 2011 - (A inverse)* ( (A) * (x) ) = ( (A inverse) * (A) ) * (x)the result is that in both cases you are left with (x)Ax/A=x and (A/A)(x)=xwith matrices you substitute A^-1(A) with Identity matrix(I) and any matrixmultiplied by an Identity matrix is just that matrix. In this case the matrix Ix=x.

joshhedgepeth Says:

Sep 10, 2011 - Are these notes saved and available for download?

joshhedgepeth Says:

Sep 10, 2011 - Are these notes saved and available for download?also, i dont understand why you bother with inverses and determinants when can just row reduce

x3ICEx Says:

Oct 6, 2011 - You can save these notes by taking screenshots of them.

joshhedgepeth Says:

Oct 6, 2011 - I do; its just tidious; I had hoped he might save them.

bebefore3 Says:

Nov 7, 2011 - iphone and ipad app for calculating matrices:itunes.apple.com/us/app/matrix-multiplication/id477093471?mt=8

khajiit92 Says:

Apr 17, 2012 - i learned to just turn the vector equation into a simultaneous equation and solve it, so i knew where this was going after watching the previous vid. the first time i've ever learnt about using matrices for anything were from these vids >.>