Khanacademy may be the best thing to have come into existence since the birth of the internet. Free knowledge, so easily obtained. You are a champion of mankind
"there is some fundamental truth, independent of our perception, that is tying all of these independent [mathematical] concepts together" -Sal Khan looks really official like this (he says this at 12:52 )
Just acknowledge this already, take it and go with it, that There Is God, your Creator, and Our Creator and Our Redeemer. and go from paganism to the Faith in One True Most High God. GOD Bless you.
I’ve been doing mathematics for 45 years and I also believe with Sal that there’s some fundamental truth that brings us all together and all of us🙏🏻🙏🏻🙏🏻
the best explanations of the matrix math I ever seen on youtube even 13 yrs later this vid has been uploaded! Khan, you're the best. Please keep doing it!
(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)=x with matrices you substitute A^-1(A) with Identity matrix(I) and any matrix multiplied by an Identity matrix is just that matrix. In this case the matrix Ix=x.
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 >.>
@tomernd1 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.
When does solving a system of equations using a matrix become quicker? Finding the inverse seems to become exponentially more time consuming as you use bigger matrices.
I believe it refers to the angle or direction. Not 100% sure though but two vectors are the same if they have the same direction and magnitude so I guess that's what he means :)
I have a question. What if an object in time travel goes on a fourth vector? Can a matrix show its domain in lets say 5 minutes? How much he "consumed" of time-space? How it looks like geometrically?
I find using the inverse to be so messy for a problem like this. I just put all the values in an augmented matrix and row reduce to find the variables. Then I just write the solution in parametric form. I paused the vid, solved it in 10 seconds and just daydreamed the rest of the vid away. ADHD = the bane of my existence.
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?
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
Khan, you shouldn't re-use your x and y variables to also be the vector you multiply the matrix of coefficients by. You should make that vector be like h and l and leave x and y only as the coordinates of your original vectors.
I couldn't disagree more. I believe seeing him actually drawing what he mentions makes things much clearer, rather than trying to cram things for the sake of time.
not really, the determinant is a scalar, matrix are normally not commutative but they commute with a scalar. let A and B be matrices and x be a scalar. is the same x(AB) than (xA)B or even
the inverse thing i didnt understand but is it right if i took the 2 equations''3x+2y=7and -6x+6y=6 and did simontanious (sry about the mispelling if im wrong)..cuz then ud find x and y plz correct me if im wrong cuz i got igcse comin xD
Khan, your platonism or kantianism disturbs me! If you knew Kurt Gödel's Incompleteness Theorem you would think thirty three times before saying that reality has a correspondent mathematical essence... I suggest reading Friedrich Ludwig Gottlob Frege, Gottfried Wilhelm Leibniz, besides Gödel, and Wilhelm Friedrich Nietzsche - not in that other, read them in a chronological order -.
Khanacademy may be the best thing to have come into existence since the birth of the internet. Free knowledge, so easily obtained. You are a champion of mankind
A champ!
I love it when Khan gets all metaphysical on us.
"there is some fundamental truth, independent of our perception, that is tying all of these independent [mathematical] concepts together" -Sal Khan
looks really official like this (he says this at 12:52 )
I actually checked the comments the moment he said that in the video. I knew people would love that quote lmao
that was a mind=blown moment
xoppa09 it was honesty beautiful
Just acknowledge this already, take it and go with it, that There Is God, your Creator, and Our Creator and Our Redeemer.
and go from paganism to the Faith in One True Most High God.
GOD Bless you.
A champ!
I’ve been doing mathematics for 45 years and I also believe with Sal that there’s some fundamental truth that brings us all together and all of us🙏🏻🙏🏻🙏🏻
the best explanations of the matrix math I ever seen on youtube even 13 yrs later this vid has been uploaded! Khan, you're the best. Please keep doing it!
These videos are so clear and easy to follow - Such a massive help to me, thanks!
Mathematics is the art of essentialism.
I actually enjoy learning algebra now... So thanks a lot ! its super interesting :D
8:06 I did say AHA!
That's awesome!
(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)=x
with matrices you substitute A^-1(A) with Identity matrix(I) and any matrix
multiplied by an Identity matrix is just that matrix. In this case the matrix Ix=x.
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 >.>
6:35 "Now, this right here...." *IS MY, SWAG.* Missed trolling opportunities
I do; its just tidious; I had hoped he might save them.
Khan please stop apologising when you go in to detail. You are a great instructor.
Becoming enlightened on this one
Thanks alot man, this is really helpful and you are a great instructor. You gave me the red pill!
Wow. These videos are life saving!
@tomernd1 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.
Helped me out alot! Got a B+ for my math test!
When does solving a system of equations using a matrix become quicker? Finding the inverse seems to become exponentially more time consuming as you use bigger matrices.
+James Cuttell It's probably just easier for computers
In Australia we covered matrices with regard to vectors etc. 2 years before college, in our grade 11. Good video though
Excellent teacher.
I believe it refers to the angle or direction. Not 100% sure though but two vectors are the same if they have the same direction and magnitude so I guess that's what he means :)
I have a question. What if an object in time travel goes on a fourth vector? Can a matrix show its domain in lets say 5 minutes? How much he "consumed" of time-space? How it looks like geometrically?
god bless creator of 1.5x speed
A champ!
Why do you really have to make this comment. to prove to strangers that you are smarter than everyone else?
I find using the inverse to be so messy for a problem like this. I just put all the values in an augmented matrix and row reduce to find the variables. Then I just write the solution in parametric form. I paused the vid, solved it in 10 seconds and just daydreamed the rest of the vid away. ADHD = the bane of my existence.
In the second step, the organization of the matrices is just one possible way of setting up the problem, right?
Nice. A bit more of the mystical stuff please Sal!
13:00 Careful now, you don't wanna upset all the relative truthers out there.
Love linear algebra
Are these notes saved and available for download?
also, i dont understand why you bother with inverses and determinants when can just row reduce
Hell yes, this guy is providing a lot of red pills. Blows my mind.
Why use the guass Jordan elimination method ?? Just wanted to have a reason behind the question
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?
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
sorry for the late reply but did u figure it out
Its been 12 years u shud probably know by now
@@rehmanmohammed9578 not yet still thinking of it
@@TomerBenDavid lmao
What does "orientation" refer to at 3:42?
Khan, you shouldn't re-use your x and y variables to also be the vector you multiply the matrix of coefficients by. You should make that vector be like h and l and leave x and y only as the coordinates of your original vectors.
Jairo Leal m facing problem regarding what u said :( could u please elaborate what you want to point out...
They are not x and y . They are i and j .. unit vectors along x and y axis respectively..
12:30 is the best part
I couldn't disagree more. I believe seeing him actually drawing what he mentions makes things much clearer, rather than trying to cram things for the sake of time.
Belive it or not this is useful for OpenGL and DirectX.
This is wonderful
It was a Matrix (movie) reference
8:30 Why not solve simultaniously?
what about the determinant -1/30, doesn't it change the result or was it already applied?
not really, the determinant is a scalar, matrix are normally not commutative but they commute with a scalar. let A and B be matrices and x be a scalar. is the same x(AB) than (xA)B
or even
Thanks a lot.
the inverse thing i didnt understand but is it right if i took the 2 equations''3x+2y=7and -6x+6y=6 and did simontanious (sry about the mispelling if im wrong)..cuz then ud find x and y plz correct me if im wrong cuz i got igcse comin xD
At 10:31 , how is 42-12 = 36?....its supposed to be 30
He said "thirty." It's just his handwriting.
Are these notes saved and available for download?
Josh Hedgepeth yes bro at khanacademy.org
The only person I can understand at 1.5x speed is Sal! I love how you're explaining it don't get me wrong! your pacing can just be unbearable hahaha
Thank you
By all means, please do get mystical on us
isn't it suppose to be -12??
cuz -6x2=-12
Sal is my hero.
Does anyone know what video 12 in the Linear Algebra playlist is about. It says private video.
xoppa09 It's a video about formal definitions of linear algebra notation
cant you just put it right into the augmented matrix?
Same question I had
I too would find it beneficial if he skipped past those sections. But, to each his own.
❤
Keep it up
you're right. the more human discover the world - the more clear that There Is One God, Creator of all and everything Above.
wow
Well yeah, but not drawing an axis, right? At any rate, I think all the downvotes on stickymage are a bit harsh.
What happened to the 1/30 :O
You multiply it to the column vector next to it and it becomes 30/30 and 60/30 which results in 1/2
there's a point to all of this... |-/
I totally had a fucking ah-ha moment. 8:05
the shapes of 6 and 0 are the same lol
666 is part of the equation.
Illuminati.
Jk.
Khan, your platonism or kantianism disturbs me! If you knew Kurt Gödel's Incompleteness Theorem you would think thirty three times before saying that reality has a correspondent mathematical essence... I suggest reading Friedrich Ludwig Gottlob Frege, Gottfried Wilhelm Leibniz, besides Gödel, and Wilhelm Friedrich Nietzsche - not in that other, read them in a chronological order -.
Is Sal a drug dealer?
he deals crystal math
use a thinner pen, so unclear handwriting!
He will go in past and do correction