Linear transformations as matrix vector products | Linear Algebra | Khan Academy

[@mikkeleriksen4568]

Sal deserves for the nobel prize committee to establish a category for teaching and then award him the prize.

[@abhishekravindra4008]

All mit teachers will definitely get this prize

[@bakhodirjonkakhkharov344]

@@abhishekravindra4008 This man changed the world. Millions of people got a high quality free education. He has contributed to the education more than any teacher.

[@lisro21]

Man this is the best explanation I have seen on this subject. I wish I had found it earlier. P.S. May I borrow your brain for tomorrows exam. This is my last math class and wont be asking to borrow it again. Thanks.

[@AdmiralPotato]

Don't know if anyone else has noticed this yet, but you just won Tic-Tac-Toe at 1:36. Thank you for taking the time to cover these topics!

[@Djskates139]

When you said "I find this to be pretty neat" I'm like what is this guy talking about and then I realized it after you multiplied the (x,y) by the vector you got from the stand bases and I was in pure shock. That is fucking awesome lol

[@OxKillah]

Thank you for doing this! Your enthusiasm makes me excited about the subject as well! Sadly, I have a terrible linear algebra teacher but I absolutely love math! I didn't do so well in the beginning but now you're give me hope and made me love math yet again! Thank you!

[@JesseDCrespo]

They should make a college where all lectures are taught by Sal himself in these videos. Shorter classes, more learning and a better professor!

[@Branhammer]

You are a miracle man! After watching this I feel like this is the first thing I've understood in my Linear Algebra class. I might just stop going and watch you cover the topics, haha!

[@Zebban89]

Thanks a million! You are a lifesaver!

[@astrophilip]

These videos are so amazing, because Khan has such a fluency with the concepts. I wish that he'd revisit these concepts in a more advanced series of videos where he went a bit quicker and deeper. But I won't complain any more than that. These are amazing.

[@staytuned7]

These linear algebra videos are saving my butt big time. They're so helpful!

[@JaySheikh22]

Khan academy is the best..I wish one day I post educational videos like u but in the fields u didn't cover yet

[@fwsGonzo]

what does it matter how many videos he has, people want to help him out because he is a great teacher =) that's probably the greatest compliment a teacher can get

[@ascahnyabute3999]

that's awesome .......am loving linear algebra because of you thanks so much

[@fh0qv74h]

This explains everything!

[@shreypatel9379]

this really helprd me to understand the concept rather than just cram up the method . Very helpful video

[@ciciwei1497]

I'm amazed, this is the most well-explained video I've ever seen!

[@ianroskow7933]

If my teacher got as excited about math as khan does, I might have gone to class more.

[@jusykes8094]

true tho

[@jetfanatic123]

i could almost not go to lecture and keep watching these videos! thank you soo much!!!

[@yiliangliang5694]

OK this is clearly my favorite (currently) part of linear algebra.

[@V4Vx]

super cool explanation, tnx.

[@s0m0c]

Gracias!

[@zelvenstormrage]

Thank you so much for your help with my Linear Algebra Final

[@mikemarachov]

You are amazing!

[@sarimLife]

Excellent explanation

[@parasrocks52]

Thanks a lot

[@muhammedafaq7158]

Good n clean explanation

[@tobiasjacobs4782]

YOU ARE THE MAN!!!

[@asf04]

moar.. i wonder when the videos will expand to cover a wider collection of university courses! I want that to happen very badly!

[@D3leriumX]

Im pretty sure he has those resources himself now. And luckily, het is not planning on stopping.

[@MrJeb123]

This helped a lot thank you

[@johnbertolon7514]

thank u so much !! It helped a loooooot !!+

[@Lyes_Abdellatif]

Super cool video👏👏👏..... From russia

[@hassaanshah490]

Thanks!!!!!And Glod Bless internet.

[@ajskilton]

@DCRosenbaum1 yup, brilliant as always!

[@dznuno7336]

Killed it, how can an amazed person describe your many kindness !!! Genuis

[@aishnaarora2642]

He is a BLISS TO MANKIND😇 Believe me ANGELS DO EXIST!

[@michaelnemov8818]

Thank you!

[@Waranle]

Thank you Sal

[@coolinglifee]

Wow there's no dislike! I might as well give one :)

[@ajskilton]

@fwsGonzo I agree, he's a total inspiration to all teachers and students.

[@kenikozo]

is it always the case to work with standard basis vectors to express a linear transformation as a matrix?

[@FRSS27]

omg this is amazing

[@chaoss5070]

thank you

[@acheacjun]

i somehow get it， the first column: 1 -1 3 is the number for x1, the second 3 5 1 is for x2, putting two columns together and times by the a vector r2 making the number assign to where they should be, which is neat

[@eamonbuckley245]

good stuff

[@Myrslokstok]

Great!!!

[@charanreddynallapareddy5418]

Great job sal

[@ChatGPT-]

Now Linear Algebra seems logical 😄

[@luismoreno555]

6:31

[@Car1ll]

@tubaplyr1 How did it work out? I have mine tomorrow :)

[@alihanbakir1604]

we are listening you with the speed 1.5. it is very fun in an educational way. thank you dayicim.

[@bokistotel]

Is standard basis the same as canonical basis?

[@kalpagarwal8291]

why are we taking column vectors as basis in identity matrix but not row ???

[@douwehuysmans5959]

Convention

[@NicoDevs1998]

Because each column represents the pivot position, which represents the unit vector for each dimension.

[@RuffRyder93]

i love you man!

[@leoncio91]

Does anyone know where I can find videos on Rep?

[@tubaplyr1]

@Car1ll Got a 85, hoped for at least a 90.

[@fernandorios3264]

Wait we don't know what x1 and x2 equal so how do we get the 3 by1 vector?

[@tubaplyr1]

Linear Algebra exam tomorrow, no problem...

[@Postermaestro]

Sal said " " but meant " "

[@wannabeviralstar]

@Assization Post more? you realize he has almost 3000 videos right?

[@1214Khan1214]

Great video, i wish u were my teacher instead of Saur -.-

[@vtn08]

That's why google donated a couple millions of dollars to them =)

[@greedypig333]

its three dog from fallout 3

[@ryand3255]

Sal, I love you

[@jr2480]

What is even the point of this? Sal just keeps hammering on this. Endlessly. Video after video after video of "matrix multiplication is totally the same as a linear combination!" SO WHAT? Why do we care? Why are we spending an hour repeating and proving and repeating and proving this one simple detail that, as far as I can tell, just makes it easier to compute transformations? Few to no practical examples. Nothing that jumps out and makes you go, "ah-ha!" Just an eternity of "This is this and that is that and I've written this expression a hundred times now, and this other expression two hundred times, but here it is again." For what purpose?!

[@ajskilton]

@leoncio91 Rep store?

[@qunayu]

Someone make this video but every time he says the word 'transformation' it speeds up

[@Wise__guy]

i love you :'(

[@eliahhigh1397]

can plz just start with an example the video is end and i understand nooooooothing at all

[@johnmartins234]

NEATO

[@maxgunn555]

@cb76tube what?

[@joshualee3054]

still confused

[@yohaijohn]

didnt understand anything.

[@Amy-tw3zh]

i totally dont get linear transformations.. i do get everything else in linear algebra.. wtf?