Basis and Dimension | MIT 18.06SC Linear Algebra, Fall 2011

[@frankshuzhi]

This is just perfect. So clear and so crisp. I used the second method myself so was kinda grateful that she explained it.

[@Oshanii]

thank you so much for showing both ways, rows/columns... I was so confused.

[@matthewshannon452]

My prof couldn't explain this at all. This video is gonna help me pass my midterm!

[@ahmadhanif1481]

Hopefully my final 😂

[@MultiVishnu55]

Which uni is this?

[@Honest-King]

So what happened ?

[@tacamos3857]

@@Honest-King Dude, it has been for 5 years past

[@isaactonui21]

😂😂

[@georgesadler7830]

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 KZbin TV with Ana Rita Pires.

[@marioleon4128]

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.

[@justkravchis8966]

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

[@akhileshmoorthy]

me too having exams, this video is really helpful and good luck to your exam

[@ruskodudesko9679]

you're a piece of shit for doin' nothing you piece of filth.

[@mostafaatif0]

6 years.. I don't think you guys still even remember how did you do in these exams

[@justkravchis8966]

@@mostafaatif0 I did well. Was a good exam for me!

[@mostafaatif0]

@@justkravchis8966 hope you all the best dude wherever you are

[@GarraOfTheFunk14]

That was the loudest "OOOOOOH" I've ever released. I finally understand

[@deepaksahoo9336]

GarraOfTheFunk14 even me dude!

[@tacamos3857]

me too in 2020!

[@munaze9281]

she finally cleared all my doubts.great job and thanks a lot

[@ajinkyajadhav2778]

Just awesome !!! Please add all videos on Linear Algebra.

[@taruchitgoyal3735]

Great explanation; I hope I get to see more such sessions of Prof. Ana Rita Pires.

[@sanketgautam4015]

Very simple and accurate explanation..... No fancy terms used 👌👌👌

[@idbekate]

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 :)

[@shivalingkoralli9474]

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...

[@Amil1173]

This is really an clear explanation. Thank you !

[@neelmanichaturvedi7901]

Simple and elegant, could not have any more simpler

[@LanoChaos]

This video is old, but gold.

[@hritikanand9734]

amazing to the point explanation

[@KatyLee]

I love this girl.

[@user-em9mw9ch3y]

Katy Lee sbian ?? ;p

[@randomdude9135]

@@user-em9mw9ch3y Ingenious

[@Astra20284]

Are you still in love with her? it's been 6 years.

[@karimabouelela3665]

@@Astra20284 lol

[@drabd3863]

please can i talk with you please

[@Historical-y9h]

After one hour my paper will be start this video really help me thanks Mam

[@BlackBears_]

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.

[@ibbsinn]

ik thats whats confusing me , there are infinte many solutions so a basis cant be formed

[@Tojasv]

exactly!

[@sarapis4375]

Finally understand what the basis is, thank you so muchXD

[@bishopvincent4308]

i am greatful to you peoples work here on u tube

[@216yogeshmathuria3]

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.

[@urielkasper]

Thanks, much more clearer than the lecture itself.

[@theawesomeme22]

thank you. you're an angel

[@effortless35]

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.

[@kewalmohapatra8340]

So it's wrong, right?

[@LesM1S3]

I decided to just listen since I was given only 4 seconds to try it myself

[@jtotherock7244]

Amazing video teaching so much to grasp easily in the big subject.

[@travolta91]

you're an amazing teacher!~ now i understand how to work with basis and span. THANKS!!~ :)

[@kimonerichards6618]

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.

[@mohammadghani1379]

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.

[@HeRotgthr]

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.

[@mirmumit1633]

whata easy explaination......... love and respect ma'am..

[@doge-coin]

Very clear. Thank you so much!

[@BlackStarSeries]

She's really bright

[@MrRykooo100]

OMG This has helpped me a lot !! THANK YOU!

[@kmishy]

Writing vectors in column of matrix is a natural form..If you make system of linear equations from vectors, you will get this matrix.

[@SanjayVishwakarmaOnline]

ultimate... this is just ultimate... thanks so much... u made it so easy to understand.

[@jacksonpark1]

She makes it looks easy! Nice

[@Dinesh_kuku]

I should have found this video earlier.. it's great

[@trading_denial]

Graet! Is there all lessons of linear algbera? Here

[@dapoogunmola7707]

Ahhh, we all feel smart watching a video from MIT Eh?

[@wencheng6626]

Finally got what it is! Thank you

[@footage6402]

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.

[@andybeyond9546]

If you have figured it out please explain it to me, I'm having a hard time understanding this😅

[@footage6402]

@@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.

[@grasshopperweb]

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.... :(

[@footage6402]

did you find out why?

[@alejandrogarciasalas2681]

more understandable than my discussion's TA and I go to another top US math school

[@pankajsharma-lp2cc]

Great work mam!!

[@ThanhPham-il1xh]

Thank you. It is very helpful and clear

[@saadiawilliams]

When you do it vertically all vectors form a basis

[@ccuuttww]

I think u should write the vectors as v1= of just big blanket the vectors

[@binnetmusayev200]

thanks for clear explanation

[@irmahernandez1839]

WOW!! Thank you so much, this was very useful :)

[@anamamer2600]

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.

[@darKnight_-_]

why cant you use the columns of the eliminated matrix? didnt understand that part

[@giaonguyen779]

Thank you! This is really helpful!

[@hanamay9132]

Why do you write the vectors horizontally like that?

[@kushalrahatkar1889]

Thnx ma'am. You helped me alot. Thanks alot

[@hdscaffe2924]

Thank you very much.

[@ashfakhalikm2444]

Superb explanation Thank you😋😋

[@paschiusaronious3734]

So would you then find the transpose of those vectors in the column space to find the basis for the original matrix?

[@mbond5358]

correct

[@fatmanurgurbuz1829]

Thank you 💛💛

[@archanapatil5504]

Very nice teacher

[@zubairsmathtutorials4542]

After taking these vectors as columns We get different basis. why?

[@henri1_96]

blessed video

[@fraze1228]

Wonderful explanation !

[@AjayPatel-te4kb]

Thank you😊

[@ScoutMcCombSculpture]

Excellent explanation

[@mikesgarage18]

If you put the initial vectors as column vectors instead are the results are the same... Hmm...

[@sasithawathmal]

simple and awesome!

[@viji001]

thanks for your videos, its was nice explanation.

[@bhanupreetham2740]

shouldn't we interchange the rows in the matrix formed by the vectors ? then we get an other basis

[@ianjoshi6778]

Can anyone explain what she did with the elimination?

[@sayandas1428]

Thank you so much mam

[@KLCII88]

Awesome video, thanks!

[@rahulverma1821]

Fantastic i am going wrong way at the starting but you clear all things

[@EFlorida121]

There's a mistake at 3:35 -4 + (-2) = -6, not -2

[@saskadiandra]

one of the reason I'm here is for the asmr

[@TheAhmedMAhmed]

elegant and clear ==> thanks + :)

[@footage6402]

going to sound dumb but why do you solve the matrix listing the vectors as rows and not columns? In graphing they're listed as column vectors. Why not here?

[@lavandelau3372]

Are those vectors column vectors in default? If yes, why the matrix does not contain four columns in this video?

[@burairabbas9301]

wow she did calculation fast !!

[@deepaksahoo9336]

This cleared my doubts

[@user-vg7zv5us5r]

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?

[@DarvinJ]

THANK YOU SO MUCH !!!!

[@abel3926]

Thanks it is very clear

[@adityam2407]

thanks a million

[@insignificantphysicist1295]

There's a mistake in the 2nd step.

[@johndemitrios6063]

You're a mistake

[@mallusajjanmallusajjan5621]

super explaining method

[@TheNsn666]

one of a hell expansive chalkboard

[@SandeepChaudhary-vx9zy]

AWESOME thank you teacher

[@ahmedanwer1767]

Amazing and thanks

[@annalam8624]

great video! thank you so much! :D

[@pathanmohmmedimrankhan2029]

Thanks

[@BeastMaster-hu4zs]

The Matlab reduced that matrix were different from her. I don't know why ?

[@issarajabu7508]

Thank mum

[@avnishsingh3181]

Helped a lot thanks

[@thobynoorhalim7976]

i'm a bit confused here, isn't the reduced form implies that it is linearly dependent, and therefore it is not a basis? (since the one condition to be a basis is the vectors must be linearly independent). cmiiw

[@aytankamienny1051]

to prove linear independence your essentially saying that x1*u1+x2*u2..xn*un=0(x is a scalar and u being a vector). the matrix in the video is a homogeneous system(every row =0) and if you reduce the matrix to echelon form you will see that the only solution to the system is x1=x2.....=xn=0. Witch proves linear independence

[@AnthonyMoody]

5:55 that was a nice 3

[@munirkhan2504]

Amazing speed sis

[@njzupdates]

In the second column method im getting 5 instead of zero in A44 and rest everything is same. Can anyone show where am i wrong?

[@stokes111111]

thank you very much