One of the great thing about your videos is that it give the learners the intuitions behind the formulars. Intuitions are some thing that very abstract and very important but very difficult to grasp. Many textbooks elaborate so much on technical jargons, which makes it harder for readers to deal with new concepts. In constrast your videos try to explain the new concepts using very basic mathematics. It's great, thank you!!
He made a mistake with C3, it should be 1/11(3c-5a+b), he forgot about b - that's why the whole answer is not correct. But very interesting interpretation - I like it :)
I'd like this video thousands of times if it were possible. This video is amazing; some of the best instruction you can get in linear algebra, period. TH-cam or college lecture hall.
I would agree with you, but I think he wants to teach it in a way where the viewer only needs to know the fewest number of topics necessary to understand the concepts behind Spans and Linear Independence. Thus making it easier for the viewer to have a better degree of understanding.
Very watchable. It's amazing how much ground you're covering as I've tried to learn this from text books before and didn't get as far. Mind you, trying to learn it from other sources will have helped me too I think.
@@siamsttr This is a video of many videos in the Linear Algebra Playlist, this video is before solving matrices solutions. Sal has a whole section of this on his website. His explaining the intuition. Hope this helps :)
Using Gauss-Jordan Elimination would work fine, I did it that way. I think it is done this way because it gives you better intuition on what he is actually doing (or what transformations are going on).
EXcelent, once i get a six figure job watching your video and passing my courses ill donate to khan academy. Best free resource, wikipedia and khan academcy
At 5:10, why do we take the last equation (in pink) and multiplies it by -2? where the "times 2 the first equation" or "-2 times C1" comes from ? What is the reasoning that gets you to this conclusion? I try to look again and again but it seems I can't find the hint for what keeps me from understanding why and when I keep going on with the video, there is another elimination to be done (7:10) by multiply the bottom equation by 3 and add it to the middle equation to eliminate the -C2.
You should have solved through Gaussian elimination. By setting up the matrix you can solve for an identity matrix (all 1's diagonally), therefore proving that there is no free variables, meaning all variables have a value independent of each other. In effect they all have their own value and they cannot have a linear combination of any other v_i.
The determinant is 11. So since the determinant is not zero, the set of vectors is Linearly DEPENDENT, though I can't figure out the algebra of which are linear combinations of the other.
Wouldn't it be easier if you put all the coordinates in a determinant to calculate their mixed production? We would get the result 9 for the determinant which is different from 0 and it means they are linearly independent
Since the first two vectors can represent each and every vectors in 3D ,the third vector must also be represented and they must have been linearly dependent but why does turns out to be linearly independent?
15:15 - But you have said that you can always put 0 as the solution for all, independent as well as dependent, right? So if I put the combination equal to the zero vector, how can that prove that it is lineraly independent? Couldn't it as well be dependent? How do I know that the zero vector is the only solution to this equation??
or you could just row reduce to find that there is a pivot point in each of the rows. Thus by the invertible matrix theorem you know that the columns of the matrix are linearly independent
So if combination of scalars times vectors being 0 makes it linerally independent. Does that mean the combination of all those vectors are only possible at its origin. Doesn't that make the span of combination of all independent vectors only the origin
Hey, u cant say that (1,-1,2) and (1,1,3) cant span R3 since R3 means a set of vectors with three entries in them and not 3 vectors. if the set contains more vectors than entries in each vector then we can say its dependent set
They are Khan academy videos. Go here and sign up: www.khanacademy.org They have thousands of quality videos on different topics with exercises and everything.
You confused me at the end when you said that system is linearly INdependent. It WOULD be if the vectors equal the 0 vector, but you only used the 0 vector as an example. What if they equal something nonzero? Would it then be linearly dependent? Meaning, I set a b and c to be 2 6 and 13, respctively. You would find c1 c2 and c3 to be something other than zero, right? That would be dependent?
You keep saying that "if one constant is non-zero then they are linearly dependent", but shouldn't it be if more than one is non-zero? Because I can't see how one non-zero constant times one non-zero vector can equal a zero vector.
I still cant seem to understand from your past two videos on linear independence and dependence what they mean. Seeing how your solutions in both videos came out to them being linearly dependent. FML
11 months late but a simple way to think about it is that if two vectors are parallel to each other, they are linearly dependent and if two vectors are not parallel, they are not linearly dependent. If you draw it out, it will be clear
I dont understand how you would get a non linearly independent set pf vectors....like obviously if you multiply everything by 0 its gonna give the 0 vector, thats obvious from the the start....
this video wasnt helpful at all...try to explain why the operations performed are used such as how you solved for a,b and c..just feedback need further explanation as to why you use certain formulas thank you
One of the great thing about your videos is that it give the learners the intuitions behind the formulars. Intuitions are some thing that very abstract and very important but very difficult to grasp. Many textbooks elaborate so much on technical jargons, which makes it harder for readers to deal with new concepts. In constrast your videos try to explain the new concepts using very basic mathematics. It's great, thank you!!
ĹBBBŞČ MÅÝ F W Ù ÑĒĒĐ ĒŞP ČÒÙŘŞĒŞ Ñ ĶÀHVÈÌÑ ČÒFƏĔŞHÒP Ñ MZ.ŞHÌDĐÌĒQÌ ČHÈÇĶİȚk...
Thanks Mr Krabs
you're my rescuer. And the part which surprise me is: you show the question may be expressed in different way. it's really cool.
He made a mistake with C3, it should be 1/11(3c-5a+b), he forgot about b - that's why the whole answer is not correct. But very interesting interpretation - I like it :)
For all those asking about forgetting b, please continue the video as it will be added and then u can continue as usual
I'd like this video thousands of times if it were possible. This video is amazing; some of the best instruction you can get in linear algebra, period. TH-cam or college lecture hall.
Thank you, I am now ready for my test on Wednesday.
So how'd it go💀
@Mehetab Tamboli that's hilarious 😂
I passed my test
I would agree with you, but I think he wants to teach it in a way where the viewer only needs to know the fewest number of topics necessary to understand the concepts behind Spans and Linear Independence. Thus making it easier for the viewer to have a better degree of understanding.
You forgot b!!
+Potpourri th-cam.com/video/9kW6zFK5E5c/w-d-xo.htmlm45s
I worked it out my self and forgot to wait. The I realized (after reworking it twice) that he screwed up XD
Hahaha it might be a New York thing but I automatically read You forgot, b
I came here from khan academy just to say this, and realized that it was already put to justice.
It was corrected around the end
Very watchable. It's amazing how much ground you're covering as I've tried to learn this from text books before and didn't get as far. Mind you, trying to learn it from other sources will have helped me too I think.
Isn't it easier to solve the equations with matrices ?
+saed ramadan
A lot of the time it is, yes.
However, this approach can cause problems if you are dealing with nonlinear equations.
but I was here for "linear" algebra
@@siamsttr This is a video of many videos in the Linear Algebra Playlist, this video is before solving matrices solutions. Sal has a whole section of this on his website. His explaining the intuition. Hope this helps :)
Using Gauss-Jordan Elimination would work fine, I did it that way. I think it is done this way because it gives you better intuition on what he is actually doing (or what transformations are going on).
What happened to the b in 1/11( 3c - 5a)? isn’t it supposed to be 1/11(3c-5a+b)?
EXcelent, once i get a six figure job watching your video and passing my courses ill donate to khan academy. Best free resource, wikipedia and khan academcy
Yesterday , i had no ideea on linear algebra, but watching this videos has enlightened me .
Thank you Sal.
NUMBER ONE THANKS PROF YOU ARE THE BEST.
At 5:10, why do we take the last equation (in pink) and multiplies it by -2? where the "times 2 the first equation" or "-2 times C1" comes from ?
What is the reasoning that gets you to this conclusion?
I try to look again and again but it seems I can't find the hint for what keeps me from understanding why and when I keep going on with the video, there is another elimination to be done (7:10) by
multiply the bottom equation by 3 and add it to the middle equation to eliminate the -C2.
Great video!
At 16:22, Salman said, that the span of 2 vectors of R3 could never span R3. Why is that?
In the "best" case, the span of two vectors would be a plane, which would only be a slice of R3.
You should have solved through Gaussian elimination. By setting up the matrix you can solve for an identity matrix (all 1's diagonally), therefore proving that there is no free variables, meaning all variables have a value independent of each other. In effect they all have their own value and they cannot have a linear combination of any other v_i.
Vincent Wilson Exactly what i did. Took 10 seconds lol
i love your videos. great stuff. this one was a little confusing with all the steps, but great work anyway.
Solving with a=b=c=0, if you have free variables, it would be dependant. If each constant equal 0, its independent.
so why didn't sal deal with the augmented matrix instead of dealing instantly with the equations!?
because in the end it gives us the same result, and as you can see he applied the same method we would apply with augmented matrices
thank you for saving me from killing myself. please never stop making these tutorials.
The determinant is 11. So since the determinant is not zero, the set of vectors is Linearly DEPENDENT, though I can't figure out the algebra of which are linear combinations of the other.
Where’d the “b” go in the c3 equation?
So simple words we are finding values of constants
You left out b in equation to solve C3
Just what I was looking for.. only I use matrices instead of adding/subtracting the equations as shown.
a little confusing at first, but cleared up near the end. thanks!!
Helpful video
Correct, he missed one calculation.
He still got the answer right that they're linearly independent. (using row-reduction you get the identity matrix)
wouldn't gaussian elimination with just a matrix work without having to write out the equations each time? Is that possible?
Yes. It is a different way of thinking about the same thing
great great video!! very helpful!
This video makes it so clear, thx
Thank you so much!!!!!!!
thank you so much , it helpled me alot.
love your voice and attitude thanks
Wouldn't it be easier if you put all the coordinates in a determinant to calculate their mixed production? We would get the result 9 for the determinant which is different from 0 and it means they are linearly independent
i think the determinant is equal to 11...
Since the first two vectors can represent each and every vectors in 3D ,the third vector must also be represented and they must have been linearly dependent but why does turns out to be linearly independent?
15:15 - But you have said that you can always put 0 as the solution for all, independent as well as dependent, right? So if I put the combination equal to the zero vector, how can that prove that it is lineraly independent? Couldn't it as well be dependent? How do I know that the zero vector is the only solution to this equation??
Amanda O my point too
amazing explanation
I always find solving these with the properties of determinants is always easier for an nxn matrix.
you are so right about that.
I knew it! Span is a generic term. It's not only related to A in Ax=b.
Thank you sir 💓
Thank you soo much , it really helps
Can you please do an example explaining the pruning of a subset!
Great video, It helps me a lot!
Everyone uses matrices. This is like the maths behind the operations. It's perfect this way... trust me.
Thanks Salman Khan!
or you could just row reduce to find that there is a pivot point in each of the rows. Thus by the invertible matrix theorem you know that the columns of the matrix are linearly independent
Can you explain relationship between independance and consistent
you are just great
Holy shit!
wonderful video
Thank you so much!!!
Thanks for these videos! It's a huge help in trying to prepare for my exam this morning. What program do you use to do the math in these examples?
USE XYZ IN REPLACE OF ABC WHILE COPYING NOTES
So if combination of scalars times vectors being 0 makes it linerally independent. Does that mean the combination of all those vectors are only possible at its origin. Doesn't that make the span of combination of all independent vectors only the origin
Isn't a set of 3 "3d" vectors going to be linearly independent if and only if it spans R^3?
Same question.
Where did the b go huhu 😭
where did the +b go for c3
+Linda Love i was thinking the same thing
+Linda Love th-cam.com/video/9kW6zFK5E5c/w-d-xo.htmlm45s
Isn't it better to use a.(bxc) to check whether they lie in the same plane?
interesting, but that only works in R^3. we want a more general method to show whether vectors are linearly independent.
Hey, u cant say that (1,-1,2) and (1,1,3) cant span R3 since R3 means a set of vectors with three entries in them and not 3 vectors. if the set contains more vectors than entries in each vector then we can say its dependent set
how do you reverse this process. I have to find the span of a matrix
what's the program that he uses for the video? im kind of sick of using paint for this kind of stuff
@dtomasiewicz Thank you, this makes more sense to me now.
I always like to imagine that its Obama teaching me this b/c he kinda sounds like him, especially when he says 'independent'
I was thinking the same. lol
Are these lectures numbered so I know which one is the first, second, etc
They are Khan academy videos. Go here and sign up: www.khanacademy.org They have thousands of quality videos on different topics with exercises and everything.
They only have 4 exercises so far for me...
wow. thanks so much! Hugs and kisses
You confused me at the end when you said that system is linearly INdependent.
It WOULD be if the vectors equal the 0 vector, but you only used the 0 vector as an example.
What if they equal something nonzero? Would it then be linearly dependent?
Meaning, I set a b and c to be 2 6 and 13, respctively. You would find c1 c2 and c3 to be something other than zero, right? That would be dependent?
couldnt you use guassian elimination? or would that not work?
@PhilChern
i think you mean smoothdraw3.
Anyone else notice the fart at 3:53? lol..probably need headphones to hear it. Great video though.
Seriously how'd you hear that?😂
theres an error! C1 should equal -3a+2c-7C3 (done by gaussian) it check out when using a vector example (1,2,3)
as C1=a-2c2+c3 does not equal -3a+2c-7c3 i think his doesnt work
You keep saying that "if one constant is non-zero then they are linearly dependent", but shouldn't it be if more than one is non-zero? Because I can't see how one non-zero constant times one non-zero vector can equal a zero vector.
Well obviously 1nzc x 1nzv = zv
10:44
Haven't seen that many C's since last months Bukaki.
What's going on? Why add a and b together? Why multiply a by -2? None of this is explained
@PhilChern it's not a "program". He is using a "pen tablet"
I still cant seem to understand from your past two videos on linear independence and dependence what they mean. Seeing how your solutions in both videos came out to them being linearly dependent. FML
11 months late but a simple way to think about it is that if two vectors are parallel to each other, they are linearly dependent and if two vectors are not parallel, they are not linearly dependent. If you draw it out, it will be clear
this is so ism - cornell coded
This made me sleepy and hungry.
what is R^3 ?
set of all 3 tuples or points in space.
xoppa09 so are we trying to confirm they exist or something?
I dont understand how you would get a non linearly independent set pf vectors....like obviously if you multiply everything by 0 its gonna give the 0 vector, thats obvious from the the start....
yeah, later on I saw that..thanks anyway...
anyone can help me whether 3x2 matrice is basis vector or not?
and right around here is when i start getting lost...
"Linearly independent if the only solution is 0"
How do you know the only solution is 0? You've only shown that one of the solutions is 0 surely?
If Ax=0 has more than one solution x, then the column vectors in A are linearly dependent.
you missed adding a b to C3
using cross product would have been better
Why did you use elimination... substitution is much better
what is R3?
Maybe an off-topic question. Why is it called span?
You should really have used Matrices in this video... Damn that was a lot of C's :P
mvp
binod
Why is he reducing the matrix in this way? Seems tedious...
is this dude canadian
this video wasnt helpful at all...try to explain why the operations performed are used such as how you solved for a,b and c..just feedback need further explanation as to why you use certain formulas thank you
im in love with you
your example is not really helpful since you used the a b c example like you did in other videos. !
thank you very much!