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

Basis and Dimension
Instructor: Ana Rita Pires
View the complete course: ocw.mit.edu/18-06SCF11
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

[@GarraOfTheFunk14]

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

[@deepaksahoo9336]

GarraOfTheFunk14 even me dude!

[@tacamos3857]

me too in 2020!

[@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.

[@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.

[@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]

😂😂

[@munaze9281]

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

[@ajinkyajadhav2778]

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

[@Amil1173]

This is really an clear explanation. Thank you !

[@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 👌👌👌

[@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.

[@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 :)

[@MrRykooo100]

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

[@urielkasper]

Thanks, much more clearer than the lecture itself.

[@sarapis4375]

Finally understand what the basis is, thank you so muchXD

[@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

[@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

[@hritikanand9734]

amazing to the point explanation

[@neelmanichaturvedi7901]

Simple and elegant, could not have any more simpler

[@bishopvincent4308]

i am greatful to you peoples work here on u tube

[@travolta91]

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

[@doge-coin]

Very clear. Thank you so much!

[@LanoChaos]

This video is old, but gold.

[@SanjayVishwakarmaOnline]

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

[@binnetmusayev200]

thanks for clear explanation

[@jtotherock7244]

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

[@theawesomeme22]

thank you. you're an angel

[@fraze1228]

Wonderful explanation !

[@sasithawathmal]

simple and awesome!

[@wencheng6626]

Finally got what it is! Thank you

[@KLCII88]

Awesome video, thanks!

[@irmahernandez1839]

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

[@giaonguyen779]

Thank you! This is really helpful!

[@damana1000]

Thanks a lot

[@ThanhPham-il1xh]

Thank you. It is very helpful and clear

[@annalam8624]

great video! thank you so much! :D

[@mirmumit1633]

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

[@bathong188]

Thank you very much!

[@fatmanurgurbuz1829]

Thank you 💛💛

[@jacksonpark1]

She makes it looks easy! Nice

[@BlackStarSeries]

She's really bright

[@hdscaffe2924]

Thank you very much.

[@adityam2407]

thanks a million

[@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.

[@hardcore5925]

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

[@DarvinJ]

THANK YOU SO MUCH !!!!

[@scoutmccomb]

Excellent explanation

[@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...

[@jasonss8363]

good explanation, thank you!

[@AjayPatel-te4kb]

Thank you😊

[@SandeepChaudhary-vx9zy]

AWESOME thank you teacher

[@ahmedanwer1767]

Amazing and thanks

[@viji001]

thanks for your videos, its was nice explanation.

[@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.

[@kushalrahatkar1889]

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

[@EsperanceBG]

thank you!!

[@Adam-gp3ij]

Thank you so much

[@stokes111111]

thank you very much

[@henri1_96]

blessed video

[@pankajsharma-lp2cc]

Great work mam!!

[@Dinesh_kuku]

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

[@arachnochim4443]

Oh boy this is so understandable! TU!

[@JoseRamos-nu8kd]

Really cool!

[@TheAhmedMAhmed]

elegant and clear ==> thanks + :)

[@user-le5my2oj6w]

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

[@avnishsingh3181]

Helped a lot thanks

[@saddamsultanakbar4342]

excellent.

[@ilgazkuscu5600]

Why are we writing them as linear combinations ? Does it come per definition of span If yes why do we show it so ? Thanks

[@madannikalje760]

Thank u very much

[@issarajabu7508]

Thank mum

[@trading_denial]

Graet! Is there all lessons of linear algbera? Here

[@ashfakhalikm2444]

Superb explanation Thank you😋😋

[@deepaksahoo9336]

This cleared my doubts

[@abel3926]

Thanks it is very clear

[@Diwakarkuldeep500]

Thanks for make this video

[@sayandas1428]

Thank you so much mam

[@shaggyzee4285]

How do you find dim, you just count the number of basis or ?

[@lavandelau3372]

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

[@archanapatil5504]

Very nice teacher

[@henripihet536]

Thank's

[@husseinmkuna428]

thanks i understand

[@brianmuchangi1315]

Thanks

[@saadiawilliams]

When you do it vertically all vectors form a basis

[@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

[@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?

[@rahibrehman4245]

in reduced echeloen form why is collumn 4 not a basis? (0,-4,1,0)??

[@kartikeychoudhary1638]

ohhh man finally understood thanks😃

[@darKnight_-_]

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

[@alejandrogarciasalas2681]

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

[@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?

[@bhanupreetham2740]

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

[@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?

[@munirkhan2504]

Amazing speed sis

[@mallusajjanmallusajjan5621]

super explaining method

[@TheNsn666]

one of a hell expansive chalkboard

[@gurleensingh4152]

Really helpful😇

[@nimeshmishra7396]

excellent

[@BeastMaster-hu4zs]

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

[@dassaurabh638]

thanx ❤️

[@khojanemoses9570]

You nailed it 👌

[@footage6402]

Do you know why dimension is 3 yet 5 components?

[@hanamay9132]

Why do you write the vectors horizontally like that?