Linear Algebra: Introduction to Linear Independence

[taekwonwelchify]

DUDE.... YOUR THE SHIT. YOU JUST GOT THE NATURAL TEACHING SKILLS... LOL FOR REALS.

[42muslimah]

aww, thanks for noticing Sal! I had noticed that videos were getting pretty long, but they're still super helpful, so I didn't wanna say anything. :)

[2011mshappygirl]

Who is this speaking in the video? God? That is one incredible voice...

[PhilNailedIt]

Awesome video, better than 'sneezing panda.'

[discy12345]

maybe you could put some links in your vids so we can find the next/previous episode easily :).

[discy12345]

thanks man!

[emejia92]

what program do you use?

[Byron10301]

@emejia92 he uses Smooth Draw and a Wacom writing tablet for writing

[TheJuga]

Thanks man the Berkeley textbooks are sort of convoluted

[fatihsaidbaran]

you are awesome and thanks for the subtitles

[qqcolaman]

So... answer me this... Why am I still paying tuition... I mean seriously... This is much higher quality of information sharing than in University.

Sigh...

[thekolbaska]

Which software do you use for the demonstration?

[guscosta1]

you make much more sense than my professor and I dont even speak english

[arpithams]

what abt vectors[7,2] and [2,3] are they linearly independent..

[SpoiledLogic]

@arpithams Any 2 vectors in R2 are linearly independent if they are non-collinear, meaning that they don't lie along the same line. [7,2] and [2,3] are non-collinear because there is no scalar that can be multiplied to either one of them to produce the other. If you graph it you can see they go off in different directions. 

[EltBerserker]

where's the 1911 button

[carrotfriend]

You have officially renewed my faith in linear algebra ;D

[carrotfriend]

You have officially renewed my faith in linear algebra ;D

[tangoforthemango]

this is awesome

[girlonlaptop]

thanks!

[LAnonHubbard]

R² detoo. It is you! It is you!

[thenekoling]

thank you!

[PoolOfTrolls]

we should replace every teacher in the U.S. by screenings of his youtube videos. ROFL

[skaai]

you are awesome sir! for those of us who are up studying at 3:30am, you are a godsend! not to mention you should rename your name from khanacademy to linearalgebrafordummies! keep breaking it down for us non-mathematics dummies! plenty of us like math, but don't speak "math" natively...

[bernicedan]

In my country (Malaysia), I was never exposed to linear algebra at all during high school. I didn't understand many things in class when I started taking first-year linear algebra at college (in Canada) this year, and you were right Sal when you mentioned in your very first Linear Algebra video that this course can seem very confusing if it's not taught in a certain way. Your videos has helped fill in so many gaps in my knowledge about Linear Algebra and I want to thank you for everything!

[jishuenkam]

@bernicedan well we do have some matrices in moderm math

[bernicedan]

@jishuenkam yeah we do, but aren't those really just basic matrices?

[luayabd]

thank you very much

[onlyAerik]

I especially appreciate some of this vector-centric teaching, and especially the matrices. I just got to a point in one of my electricity textbooks where I'm defining instantaneous values of waveforms as vectors, and they went through it fast and weird.

[Zalikify]

You have a talent for teaching, your explanation makes any topic to be easy.

[Gommaq]

what does redandent mean?

[kanitakhaled]

Unnecessary, repetitive. Already implied. Given, understood.

e.x. the use of the words "as well as" and "both" in the same sentence is redundant.

[Gommaq]

Thank you :)

[add454]

@kanitakhaled oh shut up douchebag

[TheWFDESIGNER]

Thank you very much ..

You have good way to teach ..

Kind regard From kuwait ..

[BlastedNation]

Thank you very much...something that was very abstract for me, now no matter what exercise you give me, i can THINK right and solve it not with formulas but with your explanations :) thanks a lot you should be paid for that!

[blackspoty2]

HD? thank goodness

[MrWaqasyaqoob]

you a very good teacher ,

i like your teaching style very much .

You are doing great work ,

thanks

[angelsarah7]

wow, amazing, so easy, THANK YOU

[Xlaxsauce]

you make much more sense then my professors.

[jubeidono]

Sal I'm a student now but the first thing I'll buy with my first salary will be a donation :) Thank you for these great videos.

[Waranle]

Thank you, Thank youuuuuuuuuuuuu Sal, To start again posting these Linear Algebra. All i needed.... great.

[bitchslapper12]

Hmm.. Which grade or school in USA do you study Vectors?

[khanacademy]

It is usually introduced in 10th or 11th grade in Algebra II or Pre-calculus.

[kvn89]

@khanacademy 1st year uni. for me