Introduction to linear independence | Vectors and spaces | Linear Algebra | Khan Academy
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- Опубліковано 8 жов 2009
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Introduction to linear dependence and independence
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you've helped me in grade 8 math, which was 6 years ago. Here I am in 2nd year university, and you're still helping me, but now I'm getting a math minor. =D
You just reminded me of when I was in 8.
Same here 5 years after you
@@SokumenTop now i will comment in 2026 😂
I will comment on 2027
Greeting 🙂How was it? Are you happy yo get a math minor after 6 years later?
Sal Khan is invaluable to mankind.
This guy is such a beast.... so many people would have failed their classes without him lol
Albert Einstein said(in relation to what genius means), "It should be possible to explain the laws of physics to a barmaid." Sal is a living example of that.
It is usually introduced in 10th or 11th grade in Algebra II or Pre-calculus.
Oh no
You are a godsend! I have spent all year learning about matrices and eignevalues and linear algebra and partial derivatives and not understood. i have spent 3 days watching your videos and it is clear now! thank you soooo much!
I really prefer long videos where an in-depth analysis of the topic is done. 15-20 minutes is good to take. Thanks for great stuff!
Sal my bro you are the king never met you but you one of my dearest mentors 💯 helped me through education and both life 😭😂 keep this dream alive once I graduate imma try to join your team and keep your approach to education alive
Thank you for making these great videos!! I am taking linear algebra, and the way my professor explains those concepts is very hard to understand. I feel way better after watching your videos.
You are like life saver of my intellectual journey.
I got into physics 3 months ago, and I learn all sorts of calculus with you and khan academy, and now I am learning linear algebra.
first I tried to study this new subject with books, then I got frustrated cus I didn't understand any of explanation and proof in the book.
but now after watching this lecture, what's in the book started to make sense!!!
Where ever I go to a scientific youtube channel, I will never find someone who is more satisfying than you.
Your channel is the best according to my experience of watching so many scientific vids on youtube.
Khan , Thank you so much for all the videos. After watching your videos,I just realize how stupid I was when I spent my time reading the god damn linear algebra textbook. Your explanation is very concise but very informative
Math textbooks are the worst at teaching math I swear to god I. Never benefited from them except the exercises. ._.
James Stewart Calculus and Saxon Algebra series are the only books worth a damn. The rest can be committed to the flames.
Yes, James Stewart is the best calculus book out there.
Kkkkkk just like me 😝😂
This guy can explain all of this so much better than my Professor....
thank you so much!
+ProTawN
*Typical professor:*
"Today we are going to introduce New Concept. :-|"
"This New Concept is defined by the general formula written on the board. :-|"
"Okay, so here is one example. :-|"
*Khan:*
"Hello. 8-) ♪"
"Let's talk about New Concept in this video."
"So let's say I had... I don't like this color... oh well, anyway, it will do the job. 8-)".
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.
I have a linear algebra midterm tomorrow, you're my saviour sir.
O god! U listened to me 😇Being Maths hons. Graduation student i was really struggling with this algebra n these videos of yours turned out to be miracle for me.. Thanx khan academy, u really cleared my concepts...
his voice is addictive :) god level of inspiration
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!
Thank you, Thank youuuuuuuuuuuuu Sal, To start again posting these Linear Algebra. All i needed.... great.
Hey Sal, you are fantastic. You have god gifted teaching style.
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...
I can’t believe I am still talking help from this guy even in uni
THANKS KHAN!!! IN 6 minutes you made it clear for me waht SPAN means!!!! My teached wasn't able to do so neither the book!!! YOURE A GENIOUS
It's been 4 years but i think you should see 3blue1brown's video he has great math content he also used to work at khan academy
@@pleaseenteraname1215 lol he probably graduated college and now has kids, but sure 3blue1brown is great.
Thanks dude... this is the best explanation of the concept so far and it was very much comprehensible =)
Thank you man, you have made me understand this, much better than my teacher
brilliant video, laid out the fundamentals well
Half of the semester gone, I learned absolutely nothing. today, before 2nd mid linear algebra started making sense to me from ur videos. Thanx man!! Take a bow!!!
OMG, I'm in the same boat as you. I hope I don't fail L.Alg. :(
These videos are dope. Thank you so much
Very to the power infinity nice video.. really u r teaching style is unique as well as best. U teach this using its practical significane and imagination and exactly is my way of learning anything and everything
you a very good teacher ,
i like your teaching style very much .
You are doing great work ,
thanks
Sal, you're a God's gift. And that's not an exaggeration. Seriously. How is your existence possible...
thanks! its much more understandable when u draw it out. unlike my lecturer...
Thank you for posting.
the terminology was confusing me, until you explained it properly, thanks!
An alternative way of showing that any two non parallel vectors a, and b have a span of the whole cart. plane is to first pick an arbitrary point denoted x,y, then draw a vector b * inf through that point, where 'inf' = infinity. I.e. infinitely long line through the point. Then you can show that a * inf passing through origin will always intersect with b * inf passing through the point, since non parallel lines always meet.
You explain it very well :).
My uni professor and GTA failed to teach me this simple thing- I thought I was stupid! In 15 minutes, I have realised I am not stupid.
I love you. I am in grad school at NYU for econ and you are better than the book.
Thank you!
Returning student and forgot a huge chunk of math even basic algebra😅. But still able to keep up because of youtube straight to point explanation.
thank you!
I am in Uni now, I see why people come here, your saving my Linear Midterm today :)
Thank you so much!
Great explanation
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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. :)
Should there have been '+' and '-' signs for the R set notation to specify the directionality of the vectors (vector space) ??
Given that the two vectors were either in the positive or negative planes..
Very useful
Tnx, it is now easier.
"i don't wanna do it that thick" - salman khan
you make much more sense then my professors.
"I want to get back into habit of making shorter videos"
Next video is 2 minutes longer
thank you very much
linearly dependent means that one of the vectors in the set can be represented by some combination of the other vector in the set
thanks!
you're amazing.
Hi sir. This is the first time I am watching your tutorials. They are quite interesting. But I have a doubt in the span of linearly dependent and independent set
Linearly dependent vectors spans lie over a straight line. And linearly independent spans R2 r8..... However when we considered the set of three vectors where 1 is a linear combination of the other two.....they are linearly dependent r8.... Then how come their span is R2. The concept is clear.....but I am getting confused in identifying the linear dependent and independent vector.....
Thank you :)
Bro explained this all when I just started going to school 😭❤️
this is awesome
Beat of luck my dear sir >>>>>
Thanks man the Berkeley textbooks are sort of convoluted
as long as the only linear combonation for v1 and v2 that equals 0 is when c1 and c2 is 0 then v1 and v2 are linearly independant and span V
@gommaq Hus
You mean "redundant", right?
It means that something doesn't have any meaningful purpose, and that you can safely ignore it.
For example, you only need two 2×1 vectors to specify a point in ℝ², so any extra vectors will thus be redundant, since they are not necessary at all.
good explanation
Thank u
Amazing video's! You already helped me out with Biology, Chemistry and now with Math. Thanks :)
Im watching this in 2021. I was 7 when you created this video.
@bernicedan well we do have some matrices in moderm math
Yeah that had me confused at the start as well. Go to his first video where he tells that this is just a way of representing data he could be doing it like [0,2] or like (0,2) even if its a column it is just basically the same thing. If you take [0,2] and turn it on top so that 0 is at the top it's all good. I say stick with how your teacher does it they will probably prefer it in tests. I think he just does it like this to prepare people for matrix which are later on.
You're awesome
you make much more sense than my professor and I dont even speak english
Those who have put a thumb down are really buffoons.. No one can explain simpler than this man😍
The guy that do thease tutorials, does he also do Dark Souls walkthrough? The voice is identical!
anybody know the software, that are used for sketching (black background, etc)? thank you
Thank you it turned out to be very helpful :D
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she is mine!
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nice bruh
YOU GOING TO HEAVEN AND I'LL MEET YOU THERE. THANKS
Sal khan is GOAT
what program do you use?
What if R^5? so they can't be expressed by X,Y Coordinated graph? Will you please shed some light please.
Just re-discovery of head to tail vector combination using bunch of novel terms.
Old wine in new bottles.
Wait if the matrices written in orange are linearly independent how is it that they are able to still represent anything in R2? so what's the difference between linearly independent and dependent
Give this guy my college tution fee..
Does this mean that any two set of vectors in a two dimensional plane can span that plane? 5:26 -6:20 Thank you for an amazing explaination
Actually, no. If a pair of vectors in a two dimensional plane are linearly dependent, then they cannot span that plane.
Question: Why is it relevant if they are linearly independent or not? Take the first example, even if they were independent, because there isn't a z-component of the vector, it will always only be on the R2 span.
becomes relevant later on for finding null space basis i think
5:00
Awesome video, better than 'sneezing panda.'
woow, i'm studying it now for my Computer Science degree...Thumbs up if you are to!
6:40
span the splane
Mathematics is the same anywhere in the world... It's not like languages that change dependent on country.
My gf asks, "Is that a linearly independent vector or are you just happy to see me?"
DUDE.... YOUR THE SHIT. YOU JUST GOT THE NATURAL TEACHING SKILLS... LOL FOR REALS.
what abt vectors[7,2] and [2,3] are they linearly independent..
yea
hey look there's a pivot column in every column when it's linearly independent. we're learning woo
Sal is the saviour of 99%. Humanity. Except for those 1% >140iq
how can the whole R2 plane be represented by a linear combination of just 2 vectors? the 2 vectors are essentially 2 lines no? Then how can every point in the 2 dimensional plane be represented by just 2 lines?
You can add a part of the vector to another part of the other vector, for example, if you have (0,1) and (1,0), by adding them n times you reach (n,n). Notice that n stands for any real number. Also, you can add one of them n times and them other m times. This way you can reach any point on the plane
Oh so, the 2 lines can be "scalarly multiplied" to represent any point in a plane?
Exactly. This is not always the case, try watching the linear dependent and independent videos
Dor Moshe perfect. Thank you!
👍
when you said "those three guys" you remembered me 3blue1brow..
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