Basis and Dimension | MIT 18.06SC Linear Algebra, Fall 2011
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- Опубліковано 7 вер 2024
- Basis and Dimension
Instructor: Ana Rita Pires
View the complete course: ocw.mit.edu/18-...
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
That was the loudest "OOOOOOH" I've ever released. I finally understand
GarraOfTheFunk14 even me dude!
me too in 2020!
This is just perfect. So clear and so crisp. I used the second method myself so was kinda grateful that she explained it.
My prof couldn't explain this at all. This video is gonna help me pass my midterm!
Hopefully my final 😂
Which uni is this?
So what happened ?
@@Honest-King Dude, it has been for 5 years past
😂😂
thank you so much for showing both ways, rows/columns... I was so confused.
I think if someone is actually putting chalk to board, working through an example is something very integral to the learning process. Most (not all) of my professors rely heavily on slideshows and it drives me up the wall.
Professor Ana Rita Pires, thank you for an outstanding video/lecture on Basis and Dimension in Introductory Linear Algebra. The example in this video is an excellent building block for understanding Bases and Dimensions. This is an error free video/lecture on UA-cam TV with Ana Rita Pires.
Omg,thanks so much, I am having exams tomorrow and after doin' nothing for the hole semester I can still pass. Gpod luck on exams everyone
me too having exams, this video is really helpful and good luck to your exam
you're a piece of shit for doin' nothing you piece of filth.
6 years.. I don't think you guys still even remember how did you do in these exams
@@mostafaatif0 I did well. Was a good exam for me!
@@justkravchis8966 hope you all the best dude wherever you are
she finally cleared all my doubts.great job and thanks a lot
Very simple and accurate explanation..... No fancy terms used 👌👌👌
Great explanation; I hope I get to see more such sessions of Prof. Ana Rita Pires.
This is really an clear explanation. Thank you !
TYSM!! I couldn't get this just from the explanations I got from my lecturer... only abstract theory with no practice. This helped me so much tysm :)
I love this girl.
Katy Lee sbian ?? ;p
@@user-em9mw9ch3y Ingenious
Are you still in love with her? it's been 6 years.
@@Astra20284 lol
please can i talk with you please
Just awesome !!!
Please add all videos on Linear Algebra.
amazing to the point explanation
But the set of vectors is linearly depandant and doesn't form basis, because while checking depandancy or indepandancy of the set of vectors we have to take 4 unknowns, and the rank of the matrix formed by these vactors is 3, so here rank of the matrix < number of unknowns, means that system has non zero solution. therefore these vectors are linearly depandant and doesn't form basis.
ik thats whats confusing me , there are infinte many solutions so a basis cant be formed
I saw plenty of videos on these topics but this is a good one. The teacher teaching on a blackboard with chalk gives a different feel...
Thanks for solving by Column also for a while I was afraid that my answer gone wrong that I done by column way when you explained in last then I take a long breadth.
Finally understand what the basis is, thank you so muchXD
Simple and elegant, could not have any more simpler
you're an amazing teacher!~
now i understand how to work with basis and span.
THANKS!!~
:)
i am greatful to you peoples work here on u tube
After one hour my paper will be start this video really help me thanks Mam
Very clear. Thank you so much!
thank you. you're an angel
Thanks, much more clearer than the lecture itself.
This video is old, but gold.
thanks for clear explanation
Does it matter how each vector is written in the matrix form?
Cause I notice you write the vectors as rows but others write it as a column.
She's really bright
Amazing video teaching so much to grasp easily in the big subject.
OMG This has helpped me a lot !! THANK YOU!
Great work mam!!
whata easy explaination......... love and respect ma'am..
She put the vectors into rows, not columns.
From 6:19 where she shows how to do it writing the vectors as columns. There the columns with pivot variables ended up in the basis and the columns of the free variables didn't.
So it's wrong, right?
She makes it looks easy! Nice
Thank you. It is very helpful and clear
ultimate... this is just ultimate... thanks so much... u made it so easy to understand.
Thank you! This is really helpful!
Finally got what it is! Thank you
one of a hell expansive chalkboard
Dear Ana Rita Pires
I am Ghani, from Indonesia. This tutorial video is very interesting to understand more for linear independence and basis. I just want to know the reason, why we need to prove that the vector space "linear independent" first before we call that vector space a basis? Or maybe is it related to "the uniqueness of solution"?
Thank you.
Well I think it's just to avoid redundancy, the BASIS are the root vectors together making the set and including any dependent vector will just mean including a linear combination of the root vector which has no importance at all.
Hope it helped.
simple and awesome!
elegant and clear ==> thanks + :)
I think u should write the vectors as v1= of just big blanket the vectors
Okay so the dimension is 3 yet doesn't that mean it can be graphed on R 3 graph. How do you graph a vector with 5 components in 3d space? Someone tell me why I'm wrong with all this.
If you have figured it out please explain it to me, I'm having a hard time understanding this😅
@@andybeyond9546 Ok so the only conclusion I've come to is that the dimension of the basis is simply defined as the cardinality of the number of vectors that are in that basis, in which here it is simply 3. However, we're confusing dimension of say R^2 , R ^3 as we know them with graphing just because their basis dimension is 3 in R^3, and 2 in R^2 doesn't mean that other vectors that have more than 3 components have to exist in R^3, to have a basis dimension of 3. Simply put 3 dimension space is different than thinking about dimension of a basis. Please correct me if anyone thinks otherwise.
Writing vectors in column of matrix is a natural form..If you make system of linear equations from vectors, you will get this matrix.
I should have found this video earlier.. it's great
Thank you very much.
Thank you so much mam
Wonderful explanation !
Thanks it is very clear
WOW!! Thank you so much, this was very useful :)
thanks for your videos, its was nice explanation.
Very nice teacher
Superb explanation
Thank you😋😋
I decided to just listen since I was given only 4 seconds to try it myself
Thnx ma'am. You helped me alot. Thanks alot
Awesome video, thanks!
wow thank you very much your way of teaching is awesome.
i have linear paper on Thursday i.e tomorrow and i so do not like maths and hence i didn't pay attention in classes or try the work at home and i had no idea what basis or dimensions are but now i do know a bit so i think i'll survive the paper tomorrow.
Thanks
Thanks a lot
Thank you😊
more understandable than my discussion's TA and I go to another top US math school
Excellent explanation
Thank you 💛💛
AWESOME thank you teacher
blessed video
This is not the method of getting basis vectors that I'm seeing everywhere else online and now I'm more confused. Everyone else seems to use parameters for the non pivot columns and turns the pivot columns into a set of basis vectors based on their parameter values or something. I'm more confused now.... :(
did you find out why?
THANK YOU SO MUCH !!!!
Amazing and thanks
Helped a lot thanks
thanks i understand
great video! thank you so much! :D
thanks a million
good explanation, thank you!
Ahhh, we all feel smart watching a video from MIT Eh?
super explaining method
5:55 that was a nice 3
Thanks for make this video
thank you very much
This cleared my doubts
When you do it vertically all vectors form a basis
Thank mum
Thank u very much
Fantastic i am going wrong way at the starting but you clear all things
Oh boy this is so understandable! TU!
excellent.
4:48 In which other cases, besides this case study, matrix can have a useless equation in its rows?
How you can transpose a matrix and still get a basis which is also happened to be lighter? Is it because they are in the same field?
wow she did calculation fast !!
one of the reason I'm here is for the asmr
Really helpful😇
thank you!!
So would you then find the transpose of those vectors in the column space to find the basis for the original matrix?
correct
Graet! Is there all lessons of linear algbera? Here
There's a mistake at 3:35
-4 + (-2) = -6, not -2
Really cool!
Thank's
shouldn't we interchange the rows in the matrix formed by the vectors ? then we get an other basis
Why do you write the vectors horizontally like that?