Lec 2 | MIT 18.06 Linear Algebra, Spring 2005

[NganaJHone]

I am very happy to see the vidoe Elimination with Matrices. after you give this

[Ondelendo]

Steady I Really Like This Video Elimination with Matrices

[bebeheuy]

Good, I like that you share this video, I wish success always Lecture 2: Elimination with Matrices

[willamricard]

Nice Video Elimination with Matrices That You Share , So Very Nice Thanks You

[imegatrone]

I Really Like The Video From Your Elimination with Matrices

[bundawartini]

Your Video Elimination with Matrices Is Very Useful Sharing

[anakmudajaman]

after i watched this video Elimination with Matrices, my insight is very open because the video is very good to give information

[sedlacek00152]

is this a lecture for idiots or what? for the past two lectures he said like one or two major points and he is just keep repeating them...

[smashtankful]

Sometimes I do prefer the more imaginative, romantic approach to the first several lectures in linear algebra, beginning with defining vector spaces and how operations are made, how these spaces are defined. I do however really enjoy this approach as well, it's actually a bit more applicable.

[Satoriate]

I love his flip out at 15:33 XD

[nadal0709]

good teacher~~from taiwan

[SpoiledLogic]

<3

[Dania482]

Thank you Sir, It is a great help to teach these things.

[K454R1]

I miss college :(

[RhondaJohnnyqi172]

naa ich hab was unanständiges entdeckt

[bhigr]

I love these lectures. I learned linear algebra many years ago, but this gives me a whole new way of thinking about it. Then it was just a bunch of abstract rules, now I know where they came from.

[svedishbiker]

this is awesome.

[ijbarraza]

I really enjoy this lessons as they allow me to look at mathematics from a different angle. It's nice to see it in a slow paced way rather than studying it on a rush.

[Evan2718281828]

30:35 there is a man's face in the leftmost matrix on the scren

[hnkul702]

@Evan2718281828 lol yeah i see it

[wtarantin]

@redrum41987 sorry but that's what most ppl can do :)

[drechamanjon]

Jeez that's a lot of homework

[akhil089]

thanks professor gilbert

[lolkiwi]

my linera algebra prof is so boring

[2011avalanche45]

awesome!! fantastic! marvellous!! superb!! i wish i would be there in MIT..they have brilliant teachers!!!!!

[TheRipuman]

I wish this guy was my teacher :()

[redrum41987]

He seems to be thinking faster than he can talk.

[wittsmith]

@redrum41987 You should look at his Wikipedia page. Academic awards out the ass. The guy's a math god.

[PrUnEJuIcEtHeThIrD]

@redrum41987 Right, b/c I'm sure most of this stuff is dopily obvious to him but he's trying to explain in step-by-step still.

[cebisev]

@redrum41987 man, i wish i could think faster than i can talk

[gabinobarreda]

thank you!

[shrinkingmaps]

What I like best about his style of teaching opposed to the majority is that he allows for things to come about organically and logically, instead of posting a bunch of definitions on the boards without going into theory or approach. You learn how to do things intuitively this way; the other way is just rote memorization.

[wewtneel]

Dude your awesome! haha i like learning maths this way idk why better than all teachers and coaches ive come across

Tip for students learning maths online:

watch n learn all MIT-ocw Maths lectures

watch n learn all khanacademy maths videos(there too many but still)

and ull be like king of mathematics lmao!

[zanngoc]

47:20 see you mondy :)

[orfygage]

Good professor, nice explanation, but I don't see that much a difference with my professor here in Greece, he explains the matrices just as well. The odd part is my professor linked us to this video to understand matrices better, but to be honest he could as well linked us to his own video :)

[Nedi1001]

wowww...the perfect professor!!!!!! congratulations!!!!

[pedroissler]

2 thumbs up ..

[sombra678]

freaking perfect. amazing proff

[littlemisscuddlesxx]

hi im wondering what i should do with this system

reduce to row echelon form

x1 + x2 + x3 = a

2x1 − x2 + 7x3 = b

−x1 + 2x2 − 6x3 = c

What conditions must {a, b, c} satisfy in order for the system of equations to

be consistent? If the system is consistent, will the system have none, one or an

infinite number of solutions? Determine a solution, if a solution exists, in the

case where {a = 3, b = 1, c = 2}.

[CokeJunkiie]

My uni better recruit this guy. Been 3weeks and i never got shit. A session with guy makes shit a lot clearer. I actually UNDERSTAND. Thats what's up..!

[mackazoid87]

Is the video jumpy for anyone else? :/

[finapon]

@mackazoid87 yes for me too D:

[ricsurfpro]

Thanks, teacher , and MIT, it help me a lot to understand Linear Algebra

[deryuku]

i speak spanish but, i understand very well this class

, it is incredible!!

[prusa30]

I guess this is why MIT is the best.

[MemeMachine1]

MIT professors, a grade above all the rest

[GoPila1989]

Yeah, without proofs its strange but this guy is a brilliant prof. I love him. Good job!

[qifasuineg]

No- Damn circled the wrong thing lol

[littlemisscuddlesxx]

thank god for gilbert strang

[scorpionboy3]

This is how teaching should be, and it´s the only way that it works, going from example and observation, in order to understand what happens, and then go into abstraction. Not going from presenting abstraction and applying it to an example.

[TheRusucrstn]

dap,

asa cred si eu , in cateva minute reuseste sa clarifice ce nu au reusit alti profesori in ore de predat. Oare cand o sa avem si noi asa profesori?

Apropos, eu sunt student la IT in Luxembourg si de cele mai multe ori ma simt ca intr-o scoala nu intr-o universitate uitata de lume....

Ma bucur ca datorita acestui gen de site, acest gen de profesori extraordinari sunt "disponibili" si noua celor care nu v-om ajunge sa participam la vreunul din cursulire lor.

[lyl2frd]

I even feel that I would like to cry after watching this lecture. The professor explained the thoughts and techniques of maths so clearly that makes me enjoy it very much. I feel just like watching a movie, but the movie let me understand many complex concepts.

I also found how important a teacher is! How bad some of my teachers are!

[Drodrofyl]

So... I didn't even know what a matrix was until 80 minutes ago...

This guy rocks!

[Pierzynskied]

good lecture, but still.... booooo to math

[aclamo]

this guy is a pure genius. It is a mix of Woody Allen and Albert Einstein. It is a pleasure to enjoy her classes ...

[915jefflee]

Man, this guy is soo much better than my own prof.. It's just that he's able to explain ideas much more clearly and at a reasonable pace!

[johhndough]

I love this guy. He's so funny and good at explaining stuff.

[taikukaikei]

check out the tests for this class... its insane

[MvRkc]

8 people got a F- in this class

[LoserProdutcions]

MIT > VEVO

[spectralblue]

@NothingPersonalTA Sorry third row would then be -5/2

[rinwhr]

5:26, he said he is going to subtract, how is 3(2) - 8 = 2 and how is 3(1) - 1 = -2??

It should be -2 and 2 respectively

[spectralblue]

@rinwhr He subtracted 3 x row 1 "from "row 2. That is 8 - 3(2) = 2; 1 - 3(1) = -2.

An easier way to think about it instead is multiply row 1 by -3 and add it to row 2. People find it easier to add instead of subtract when negative numbers come haha.

[slatz20]

why someone is interested to change columns?? it doesnt make sense to me.

[MobiusCoin]

"And died earlier too..." LOL

[NothingPersonalTA]

Quick question: Could the -2 of the 2nd row have been selected as the pivot instead of the 2?

[ankit2801]

@NothingPersonalTA no it cant be as the pivots are the elements in the diagonal of the matrix.

[spectralblue]

@NothingPersonalTA Well technically yes if you exchange the 2nd and 3rd row. Pivot point on the 2nd row would then be 4, third row -2. Row echolon form is not unique (meaning how you solve it and what numbers will show up depend on the person). However, once you reduce it, RREF is unique (solution should be the same for everyone).

[NothingPersonalTA]

I will be watching all of these lectures during the break. Hopefully I survive stress analysis the second time around...

[qpham26]

I think khanacademy did a better video =) just my opinion, this video is helpful also =)

[diegogerardoandree]

I am that guy who asked after the class.

[hafrox]

@diegogerardoandree Oh yeah, and what did you ask?

[SpoiledLogic]

@diegogerardoandree Oh haha that's great. What did you study at MIT?

[adidasguy87]

"No, damn! I circled the wrong thing." This guys great

[DracoRenaissance]

if this professor's class would be a column vector, it will definitely be linearly independent of all other linear algebra classes. He squeezes in new and interesting stuff that is not in the other vectors

[periblem]

Are the subtitles are shifted 3-5 seconds or is it just me?

[overred2010]

tmd,讲的太好了

[chuckbiss]

is there a way for me to see the HW problems?

[5w33ti3]

I took 18.06 from a different prof, and I have to say that at the time I mostly learned from the text, Strang's book. Strang is simply excellent at explaining linear algebra (I'm a math teacher now and taking ideas from these lectures). Thank you!

[heyyodoug]

Doesn't Youtube only allow for 10 minute videos?

[Nityananda108]

@heyyodoug MIT hackers broke the code.

[heyyodoug]

@Nityananda108 did they really?

[Nityananda108]

@heyyodoug I was joking, MIT has made a deal with Youtube,  otherwise it would be frustrating to watch 15 minutes episodes of a lecture.

[cesarizanami]

I dont speak good english , and I understand him, that´s AWESOME!!, dont you think?

[belakv]

If only I had a teacher like him! I see now maths can be interesting, funny and easy;)

[torroxceles]

16:45 should be a 10.

These lectures are amazing! I've learned so much from these videos. :) And the professor rocks.

[aqcpatrick]

@torroxceles its -10. the dude is correct.

[torroxceles]

@aqcpatrick, my bad. You're right, -10 is correct.

[dorourke4114]

This is so helpful, the whole series. My professor can't teach his way out of a paper bag. I finally understand all of this! These videos are how I am passing my math class! Thank you!

[samuel91222]

Great prof..he makes linear algebra makes more sense, and easier to understand..I mean it is suppose to be easier..the purpose of linear algebra is to make complex thing easier to solve...but unfortunately many teachers dont teach it properly, making it seem so hard to learn

[anubis656555]

this should be called mr. rogers teaches mathematics

[tubeyouler87]

NO!! lol it's funny when he makes a mistake

[andrewrosso]

i wanted to see what was the question of the guy at the end there. maybe it would solve my question

[samson4474]

This is a great series as so much of understanding math comes from the instructor's ability to convey the material in an understandable way. I have a very intelligent instructor at my university, but he does not take an intuitive, step by step approach. Many students are therefore left scratching their heads and trying to make sense of the text, which is bad enough. These videos have been invaluable to me. Thanks for posting them!

[FrukSkoFcsae]

lol this guy taaaaakes his time. Our prof explained all this in 3 min.

[zkhandwala]

I find it interesting that there were ~278,000 views of the first lecture, but only ~90,000 views of this one... I wonder if MIT has that sort of drop-out rate ;-).

[Waranle]

@zkhandwala only the one who can efford :)

[bp552001]

Not only is he a great professor but a great author too.. I already had a Linear Algebra text but bought his book anyway and it was well worth the $80. The way he sort of asks himself questions then answers them to simulate what the students might be thinking is very effective, and he does that throughout the text the same way he does in the lectures.

[davidgonzalezherrera]

Such a shame education system in my country is as archaic as The Flintstones, although they have a better education than we do here, and well, what can we expect, Spanish invaders brought thieves, scum and crap to our continent.

Long live America.

[alquiora]

Hahaha I feel pity for the Professor... explaining algebraic calculations is super tricky

[fasantupp]

the 7 dislikes are wierd.. cus if you like math i dont understand why you wouldnt like the video... and if you dont like math... why the hell would you view it?

[kevinkuei]

@fasantupp Your assumption that everyone who watches these videos must inherently enjoy math is misguided. I watch these videos to supplement my math classes or to get a better grasp of the material before class. Is that implicit that i enjoy math? Is it reasonable to say that if I enjoy math, I must thumbs up this material? Not saying that I did, but anybody looking for the extra help and feeling like this video was unsatisfactory to their tastes would dislike it. Nothing weird about that.

[fasantupp]

@kevinkuei Yeah, i see your point, everybody got different taste. But imo the Professor explains everything very well, so if they are unsatisfied with this video because they didn't learn enough maybe they should consider taking another class.

[paytontech]

@fasantupp Some folks HAVE to take math even though they don't like it so they view it seeking help. I love math when I'm using it to build something or understand something specific in the real world but otherwise I don't enjoy it. That said, this guy is really good. I haven't had LinAlg. and don't have a super math background but I learn from him quite well.

[kotofu]

@fasantupp stop trolling. Are you saying that someone who likes math with like every single lectures about math? I dont even know why I bother answering your semi-rhetorical question. You are clearly just trolling

[fasantupp]

@kotofu Ofcourse someone who likes math doesn't need to like every lesson, but the only reason to view this is to learn something, and if you don't learn something from this it's probably because you have already studied this, you aren't on this level yet, or you are just stupid. Theese things are your own fault (possibly parents) and there is no reason to blame the video.

[fasantupp]

I get so happy when things like that look kinda hard in the beginning solves that easy just because you know how to do it :)

[psbjr]

37:17 that's what she said. . .

[xboxMontagers]

@psbjr did you really just watch a 47 minute video about Linear Algebra, and out of it you get a thats what she said joke??

[psbjr]

@xboxMontagers that's what she said. . .

[0nti]

These lectures are wonderful, I really appreciate the time people take to give this for free, it's awesome.

Thanks!

[vedik101]

I got 0 0 -5 too. I don't know if we're right though?

[harryhuang999]

at 9:27, does the equation 3 be 0 0 -5?

[steal88]

@harryhuang999 3rd row is correct, because You multiply 2nd row by -2 and add this to what You have in 3rd row. So 4-4=0, and 1-(-2x2) equals 5.

[MrDogbert2]

Professor Strang is the f'ing man!!!

[Treshor]

Gosh this guy explains things very well. Im taking this class over summer right now and my teacher has a super heavy french accent. I wish I had time to watch all these lectures.

[sikory]

36:20 anyone know who the autor is? :-P

[Gaiacarra]

@sikory The author of the textbook.

[sikory]

@Gaiacarra yeah i ment the writer of the textbook, look at the course site who it is.

[longhorn4500]

I want in MIT ! Please take me there :)

[skyfaze]

such a down to earth professor and speaks in such a friendly manner(Y)

[CEZA14n]

WOW this teacher is great....YEA no wonder he teaches at MIT...i have a shittty teacher wich makes this material 10X's harder

[insanity152]

@CEZA14n dude be thankful , we do not have a professor we have the exam finally lol

[d7me]

15:37 "OH DAMN ... circle the wrong thing"

great professor .... mistakes happened to all

[Apexare]

Beautiful! I guess that's why he's a professor at MIT...

[fesaco182]

That's right... I speak spanish but I understand this better in english with this professor.

[flashliqu]

Hey, the closed caption just disappear once the word is showed, It should continue to appear until the next word change. And audio and video is not sync either.

[007pooji]

ohhhhh my god

thank you sooooooo much sir !!!!!

i dnt believe dis is freeee!!

[FarrenfollowsBen]

this guy is so good he makes me want to cry

[trousien]

that was beautiful... this guy is better than all my math professors combined... he is so good at explaining things that i can walk into my midterm in 4 days and feel confident... i didn't understand crap before listening to this dude because my professor was just horrible at explaining how matrices and operations worked but this dude makes it so clear and makes it faster than reading the book

[smileandlaugh123]

Thank you!!! This is great help.

[MomosReel]

bddk 18:17 break time yum yum

[skyfaze]

great teacher (Y) very friendly

[MomosReel]

at 10:29 he is showing a 5 in the (3,3) position. Is that suposed to be a -3?

Is that right?

-2(2) + 1

Sorry i'm just not very confident with math so this is just me not understanding the super basic opperation here.

Plus I'm tired right now after a calculus final.

[TheMozarka]

Yes, he is correct. Since the multiplier for row 2 is 2, you need to multiply what's in the (2,3) position by 2 and subtract it from what's in the (3,3) position.1 - 2(-2) = 1 + 4 = 5. Hope this helps!

[MomosReel]

Oh, silly me. We're multiplying by neg. two. Clear as day today. Thanks.

[mloskot]

@TheMozarka It doesn't seem quite right, because the multiplier for second row is 2 not -2, as long as I can understand the lecturer properly.

[kauigirl808]

I can hear quite fine on this lecture but not lecture 1. Very strange.

[yayatrista]

I like the way he presents the lectures.He explains the problems very well.

[izi2bhappy]

this guy is awesome, my english is not that good but i somehow manage to understand him clearly! thank god for this lecture and for pause bottons!

[in3d8field]

Great teacher. Wish my instructor could explain the concepts like he does. Wasted some time wondering why we were doing those problems. The concepts are so important.

[ginteardrops]

My teacher is TERRIBLE! Thank god for these videos. I may actually pass my final now!

[bingarad]

hhhh, I have the same problem... My prof is the worst prof I have ever seen in my life.. you cant imagine how boring he is!!!!!!

[AtanasNenov]

"You get an A in the course." Hahahahha. Not only does he give an amazing lecture, but nice sense of humor as well. 5/5.

[petelite]

Yes, because "writing special erasable marker" expresses much stronger academic competence.

[Shakespeare1612]

I agree though. They should have Interactive white boards and project computer simulations. They should be interested in presenting the information in as clear a way as possible. In video 1 he even appologizes himself that his art work can't keep up with his imagination. And if I didn't already know a lot of math that lecture would have been complete giberish, mostly due to poor visial aids. The professor's is a math genious. That's not the question. The question is, does he was to teach or not?

[geffara]

The most important is the Students NOT the Stuff in the University or the Multimedia Sources.

The Most important thing to force students understand the concepts .

Thank you

[calekl]

I agree about the chalk, really. I find myself so tired of looking at a computer screen, and having to deal with the 32 or however many flashes of light per second day in, day out. Somehow the teacher feels more present and more connected to the material when using chalk, I think.

I dislike online assignments too.

[1V10ntyPyth0n]

chalk rocks!

[mertert]

this was recorded in 1999.

[mixxmexx]

is that why it says spring 2005?

[mertert]

i dont know why it says spring 2005. this was recorded in 1999.

[mixxmexx]

teacher are so conservative..good point, thought about that too

[doubleja]

"AHHH, sorry he's still there"

^.^

[avansc]

not sure why MIT is so revered, this is almost verbatim what i had in my linalg class. i suppose the research is where its a bit different.

[thou9009]

There are good instructors everywhere, of course. I think it does have to do with the research...among other things.

[TheEarlOfDublin]

this is rudimentary stuff, its taught the same everywhere. Did you expect them to telepathically transmit the information?

[mmasny]

sure it's rudimentary, but it's certainly not taught the same everywhere. Teachers are different. I remember my teacher and he couldnt even compare to this guy. It's the matter of preparation and speaking skill.

[ZemrusheD]

I bring my mac to class, open it and watch these lectures rather than watching my professor lecture. I save more time that way :) haha

[Frostfirepenls]

Thank you! The only thing my linear algebra teacher does is prove things. I have no idea what to do in the class, but this helps me greatly. After watching and rewatching the first few lectures here a few times and doing example problems in my textbook, I am fully caught up in my class.

[supaflyjohnson]

Gilbert Strang is a golden child.

[stop190]

Not that I care. But why do you whatch this then?

[T3HMUFF1NM4N]

how on earth did you make it to the second lecture if you hate math?

[sHART1780]

I didn't watch the first one. I just checked this out real quick to see if I understood any of it.

[eblusyon]

amazing video! now i can not go attend my class! =)

[KH2083]

I think he presented gaussian elimination very clearly. It's important algorithm for example in the process of inverting matrices

[alvinleeal]

he made elimination to complex

[doanthanhnam]

It's such an amazing video. He made me know the real meaning of matrices, not just use it to compute