Lec 2 | MIT 18.06 Linear Algebra, Spring 2005

[johnny84628462]

in germany we learn that in high school ....

[notoco998]

in Germany we SHOULD lern this in high school

[connectslayerbananas]

we do too in england

that is AS/2 level tho

so not in this much detail

[psychobollox]

fuck that ... n x n NON-ZERO matrices.... THEY form an Abelian group...

note to self: put the tylenol back now....

[psychobollox]

nxn matrices form an Abelian group.

[ganondufus]

Well at least he's speaking english. When I took this class, my prof was Chinese and had the thickest accent ever, lectures were useless, I learned everything from the textbook.

[peter56789101112]

What a brilliant man. Can you tell he fences?

[octazagarin]

he's a bit slow and he's babbling.. I had better teachers in Romania-University Pitesti of Computer Science. What he teaches s basic....they should have known that from highschool

[Nisshoku1729]

No shit, he even says it's "such as basic algorithm and you know it"

Every class does this at the beginning of the course.

Even the ubiquitous "Feynman Lectures on Physics" starts off with a review of elementary calculus.

[psychobollox]

what you're forgetting is that many may have not done this at high-school and so a period of balancing studies would be required, to get everybody onto the same page, for when the REAL linear algebra work begins!

also, the course is billed on the MIT site thus:

"This is a _basic_ subject on matrix theory and linear algebra." (my emphasis)

Grow up!

[johnny84628462]

yep i believe you because in germany and poland its also subject matter from high school

[octazagarin]

the last pivot is 7 not 5

[rhammes07]

I just have to say this, I'm taking college level Linear Alg. I, and this professor online has taught me more in 2 lectures than my current prof. has in 10 weeks. Please let me into MIT! haha

[chirho23]

I've learned solving linear equations by applying elementary row operations on the augmented matrix. Watching this video made me realize that this row operations can also be expressed as matrices. The Prof is great!

[KarenisDestructive]

Thank you soo much for clearing up a few errors I usually make when trying to reduce the matrices.

[nysabydee]

Nice

[polysonic]

THANK YOU so very very much to whomever is responsible for posting this! This is so great!

[AshikaUmanga]

whar are the criteria for selecting Pivot ?

[KarenisDestructive]

Pivot is the first integer in the first row. In the second row, it is the integer below and to the right of the previous pivot. And so on...

[psychobollox]

so, the pivots are the (non-zero?) elements on the main diagonal, then... yeh?

my lecturers never referrerd to them as pivots so that notion's new to me... not arguing that it's wrong... just saying our guys never used the term.

i can see why the term would be used for these elements, though!

[bigMcman]

this guy is an absolute hero. I dont think you guys realise how lucky you would be to have someone teach lin alg this well.

[BugByte1000]

I totally agree with you :) he is just awesome!!!

[ewha1]

Completely agree. He's great. Makes Maths so wonderful. I had a very good Prof at uni too.

[mexicanyutub]

.

Vaya hasta que hay videos de provecho en la red. Felicidades y tambien dejenme decirles que he encontrado un sitio llamado

wannasol com

ahi hay videos también no como estos pero puede ayudarles en sus clases de matematicas.

Saludos

[sairinlote]

publishing lectures of any scientific field is or vital importance to the progress of humanity :) I support this action 100%

As for the teacher, my only comment would be that he lingers too long on a topic for my liking. He is thorough but to an unnecessary point. Maybe the next videos will change my mind!

Nice work though :)

[panteamoshiri]

i love algibra

[CogitoErgoCogitoSum]

OH MY GOD. I cannot deal with this guy. He is just winging every lecture by the seat of his pants... no lesson plan and he cant speak to a crowd. He keeps referring to things that he hasnt lectured on yet as "what we arent going to be doing today". SHUT UP and get to the point!

[epicswell]

Its just his style, I think you are being a bit harsh there. I doubt one gets to lecture at MIT by 'winging it'.

[CogitoErgoCogitoSum]

Dont be so sure. You dont need to have a teaching degree to teach at a college or university. The only requirement is a Masters in the subject. That is true in this state anyway. You dont need to be a good teacher to be a skilled mathematician, and the demand for math teachers is higher than any other... so they'd hire anyone. Consider now that this is a tech school and not a university. Does the masters requirement even hold? All you really need is a reputable history applying the material

[CogitoErgoCogitoSum]

Now, the guy that does the Differential Equations lecture is AWESOME

[psychobollox]

"Consider now that this is a tech school and not a university. Does the masters requirement even hold? All you really need is a reputable history applying the material"

generally, yes... a master's degree is usually required, although i do know a guy teaching in a university of applied science and he has a BA (Hons) in his field, with a lot of experience in the field of his degree. it would seem that a requirement can be relaxed if the applicant has other relevant things to offer.

[CogitoErgoCogitoSum]

So first you tell me that Im wrong, then you cite a personal example in which I am proven right? Im sorry, what was the point in you posting this response? Just like seeing yourself online?

[psychobollox]

what's your problem, cunt?

i was trying to amplify your point on the general requirements for a master's but that this can be waived for other reasons.

what the fuck is your problem with that?

jesus fucking christ!

[aaronhallam61]

He has it all planned out, but his style is to do a little acting in a way that mimics the mentality of the student. I think it's effective.

[Junosdaughter]

Thank-you MIT I love your math and science lectures.....more to come please? ;-)

[Skurgefaust]

dam, this is so cool!!

[Pferdekopfnebel]

this is so helpful for me :-)

no more searching in my exercise book

no boring reading sessions

just watch the video, pause if you need a break and it's all good :-)

[kitchen7658]

This is basically RREF

[asphyxiateDrake00]

Haha I remember doing this shit in Algebra 3/4. So tedious lol.

[aikudo]

best free math lecture! :)

[kowphoot]

did not like his lecture, a tad to sloppy

[troponinnutrition]

'too'

[afghanA00]

lol nicely done.

[kitchen7658]

I agree..

[fregoso2027]

i dont get this matrix tho...

3-3x1 =0

8-3x2= 2

1-3 =2

..why he said to subtract?, am I wrong?..didnt litsen correctly?..or just because im mexican..haha

[astroquick]

he wants to eliminate the 3rd row, 1st column entry of the matrix so he multiplies 3 to the first row and subtract it from the second row.

[MatrixHeat7]

he have a mistake in eliminated second row ,there must be 0 -2 2, not 0 2 -2

[MatrixHeat7]

dont care , i was wrong :)

[fregoso2027]

woooooooooooooo!...free lectures..no need to pay some $28k bucks..fuck that shit..cuz im mexican cuz..ahahaha..lol

[milo223]

lol but where is your degree at?

[celisto001]

what does it matter if you didnt pay 30k or whatever it is, you still have no actual documents of your degree to provide to get hired..

[b0bb0bs0n]

these lectures are awesome!

but that professor makes me laugh

lol

[SpicyHam]

very very easy.

kindergarden stuff

[dhyanabum]

you moron...

[SpicyHam]

who is the Pre-K moron?

[dhyanabum]

You are one of those people more concerned with being smart and thinking about how easy things are for you than the actual mathematics. There is always someone smarter, so try focusing a little more on the stuff and less on yourself and you find that even the "easy" stuff can be deep and interesting. :) Didn't mean to offend you before, I said "moron" in a jocular way, because I've met a thousand people like you...

[SpicyHam]

and therefore u have the right to say that?

u pathetic fuck

what if i am actaully the best?

u r dead.

[dhyanabum]

I'm sorry, it was stupid of me to say that. I admit it. But why get so riled up, if you were really "the best" - rofl - I'd be pretty confident and I think I could shrug off a "moron" comment with making death threats... ;)

[dhyanabum]

without*

[SpicyHam]

yeah i think i should let people steal my food ;cause i am really the best

I also appologize for my rudeness. Internet is a messed up place.

[jefflehman]

At MIT they are paying for the small class sizes and good teachers.

[sassoleo]

This guy should teach the teachers. Two hours with him were worth more than a month at school.

[alimad89]

i agree 100% he is awesome !

[darney1234]

if there were more teachers like this guy ,

people may actually look forward to going to classes .

[alimad89]

yea man , i stopped going to my classes... all i need to do is to watch these videos !!!

my university sucks !!!

[jnicelap]

Can anyone tell me how to find A when you only know the inverse of A and you also know b. Ax=b. Thank you for your help

[rjm5062]

It is not needed to know b. Just take the inverse of A^-1. If A is invertable, then A^-1 is invertable and yeilds A.

[Jeslinh]

tell me if i'm wrong.

He mentioned about Subtraction, and how did he get the second row (ie: 0 2 -2)?

3*1 -3 = 0

3*2 -8 = -2

3*1 -1 = 2

the second row should have been 0 -2 2.

I dont understand why his students didn't point out his error.

[ezsanche]

There isn't a mistake.

3 -3x1 =0

8-3x2= 2

1-3 =2

You had the numbers backwards

[DOS32]

I think I ever heard his name.

[DMK000]

Thanks for uploading these. They really give me a feel for what linear algebra courses are like.

[apta216]

I cant do basic algerba, AM I RETARDED.

I AM IN COLLEGE BUT I CANT DO SIMPLE MATH.

[batteekha]

Well sorry but yeah :p I can help you though

[batteekha]

Why isnt it available anymore?

[mi8nu7by6]

Gaust given order- LOL!

[MathMikie]

i discovered this method myself when i was only 16 years old

[gaga2929]

happy birthday

[ArabicPilot]

1:40 "the idea of elimination is...you would have thought of it."

con-friggin-gratulations, my friend

[EnderMB]

I think these lectures are fantastic. My university offers only basic Discrete Mathematics at undergraduate level for its CS students so these video lectures are literally saving my ass from being a failure.

For those claiming that Prof. Strang's methods aren't that great you can easily tell that he has this entire lecture already planned in his head. Remember that he's teaching undergraduates at one of the best universities in the world; I'm pretty sure they'll handle Linear Algebra with ease.

[Jonnymont]

i agree these are fantastic

go MIT

[Monkeyradar]

I'm sure that there is another prof at your college that teaches just as great as this guy. I do not know your prof for linear algebra but I'm assuming that he does know what he's teaching. He just doesn't know how to teach it. It isn't good when a prof cannot teach but I do have sympathy when I see them try to get it in our heads. Us students also have to pull our weight when learning.

[Monkeyradar]

I got rejected from MIT but it seems like this dude is just like any regular professor for linear algebra. Well I should say more than regular because some profs suck. Bottom line is what makes MIT so special beside the ratings. Teaching is basically the same.

[brco2003]

ignor

[Monkeyradar]

What's that supposed to mean? I'm just telling it like it is. I think that he is a good professor but there are people just as good in other colleges with not so high ratings.

[dudeman209]

He's better than my linear algebra teacher. My teacher is an asshole who can't teach shit and doesn't know what he's talking about.

[legendy2j]

wow i love how he makes this course feel like basic algebra lol. thanks you mit i am getting ready for college with these videos.

[adcegar]

you cant match all tastes. Ever.

[jahdallah]

Prof Strang is really fucked up.

[gadicherla]

Prof Strang. The lectures are great and have clarified long forgotten concepts of linear algebra for me. Wish we had profs like him in our university.

[JackMRich]

1--4 with you ... !

[miarizza]

1 - (-4)=1+4 = 5

[JackMRich]

I Didnt go to big school but i understand what he is teaching except how he got 5 in the U matrix... can any one clarify in a sentance please?

[brco2003]

He did the bottom row minus middle row. 1-(-4)=1+4=5

[2terence2jones]

1 2 1

0 2 -2

0 4 1

He subtracted 2 times the 2nd row from the 3rd row.

So it's 1 minus 2 times -2, or 1 minus -4, which gives 5.

[RandyQuaid]

If you can't understand this guy, go back to your computer science (oooh, python) and leave the math to the Mathematicians.

[miarizza]

1 - (-4)=1+4 = 5

[SteveCrank]

many thanks , this is good for the whole mankind :D

[laxrox1093]

uhh Mr. G Strang,

these r kinda unclear

[purplekitty627]

I listened to this lecture while I was doing my Linear Algebra take home test. It probably wasn't exactly the same thing that I was working on, but it helped me out. I had forgotten about exchanging rows.

"What if we don't want to do anything?" Then don't do math! LOL j/k Whether you write something down or not you are working, because it's still mental. It's just not "working" according to the "Physics" definition.

[purplekitty627]

I wish that our university did this.

[mitchchoiSK]

no I know how fucked up my proffessor is. Mr. Stlang. U are my master jedi.

[frankfurt28]

These MIT lectures are just great, wonderful, I think there is no adjective to express this. Just superb...!!! If I only had someone in my life who taught me like this... Not difficult to become an Einstein. The depth and insights he gives...!!!

Thank you very much for posting these lectures... Being reeducated again!!! Is this professor also a researcher? Just GREAT!!!!!!!!!!!!!!!!

[jonahansen]

Gilbert Strang's book is one of the best. I always wanted to see him in action! Thanks for the video...

[cdprop]

Thanks to Professor Strang. I am learning a lot.

[rehxyz]

Wait, I don't get it. What's the procedure for elimination? It feels like he completely skipped over that--or maybe I'm just stupid.

[skulduggerous]

Basically, you eliminate all values (vertically) "below" the pivots, so you get reduced row echelon form. See wikipedia on Gaussian elimination.

[uchihay2g]

Every school does it differently. My school started with definitions of linear Eq. Very terminology based. This helps also. Instead of calling it elimination, we called it reduced row echalon form. Somethings he says, I have to look in my book. He goes straight to examples which I think is more helpful than definitions and proofs like my school. : (

[honeybbqgrundle]

Well they still have to know the definitions at MIT even if he doesn't emphasize it (although he's pretty good at defining everything in class). As far as proofs are concerned, he does proofs but sometimes they're not as rigorous as a mathematician would want. This course isn't just for math majors. It's for engineers and CS majors as well and they probably don't care as much about proofs as a math major would. Maybe your class is geared more toward math majors, which would explain the proofs.

[pantoum]

There was no explanation of elimination here. It seems to be implied.

[RandyQuaid]

Pretty sure you cover basic echelon elimination in Pre-cal. At least I did...

[eckz59]

What I think everyone can agree on is that this professor, although obviously a genius from the list of accomplishments below, is not good at being a professor. It is difficult for a college freshman like myself, who is trying to learn linear algebra before I am even offered it, to remain attentive throughout the stumbling that is this man's lecture. I continue to watch simply because I am too lazy to read (especially since I am doing it on my own initiative, and not yet for any course.)

[honeybbqgrundle]

If you're too lazy to read an algebra book along with these FREE lectures, then you have no right to complain. You call that initiative?

[eckz59]

umm... yes. I don't have to be learning Linear Algebra at all, but I am. I call that initiative. Plus, maybe I don't have money for a textbook. As if I'm not already taking an extra class this semester for an early Master's - you don't know me, so mind your own business

[honeybbqgrundle]

Are you learning it? Seems that you're complaining about a perfectly good lecturer because you're admittedly too lazy to open a book. There are free linear algebra books online, or you could get the excellent text by Shilov that costs about 12 bucks. Just don't expect to make unnecessary criticisms and not be called out on it.

[pantoum]

Why are you acting like a rabid ShitBitch? I stumbled upon this video and decided to to watch it for fun. I must say that although I can gather some vague notions of the topic this speaker, how ever decorated he may be, is leaving out some vital aspects. This lecture is far from exhaustive, and novices will have to look elsewhere for further explanation.

[honeybbqgrundle]

Since when did lectures become completely exhaustive? All those students had a BOOK which they read on their own time, just the way it's always been. Of course if you don't have a book you're going to be lost. Take some responsibility and stop blaming the professor when anyone with a brain can see that your "vague notions" are entirely your fault.

[honeybbqgrundle]

And sorry for being a "rabid ShitBitch" lol, but you're blaming the wrong person. Get a book and read along and you'll get a lot more out of these lectures.

[yahelordie]

shut da f... up eldeodoranto...

[Eldoradotrueshot]

MIT does Gauss elimination on Lec2 ?? , I thought Americans student were born with it.

Anyway he didn't check his determinant was different from 0 at the start. And he speaks about invertible matrices even when not explaining his word..THIS TEACHER IS FAIL

[gorgod]

Him:

Alfred P. Sloan Fellow (1966-1967)

Chauvenet Prize, Mathematical Association of America (1976)

Fairchild Scholar, California Institute of Technology (1980-1981)

Honorary Professor, Xian Jiaotong University, China (1980)

American Academy of Arts & Sciences (1985)

Honorary Fellow, Balliol College, Oxford University (1999)

Honorary Member, Irish Mathematical Society (2002)

Award for Distinguished Service to the Profession, Society for Industrial & Applied Mathematics (2003)

you: flaming douche

[nealtuf]

Excellent.great teacher, thanks!

[higiraven]

i think he's a very good teacher.

[ken62310]

so hard to understand.....

[picajoool]

Agree :-)

[picajoool]

Hes probaly a genius in maths, but his an terrible narrator and that leads to problems when passing knowledge to another person.

[containedintwowords]

Its not very hard to look past his communication issues. He is quite consistent in how he stumbles about.

[honeybbqgrundle]

I don't think he's bad. You can tell that he wants to say so much, because there's so much going on, that he has to decide what to hold back and save for later. Besides, this isn't high school where it's very possible to do well in math without really reading the book. In college, if your lecturer isn't the best, then you have to be able to learn a lot on your own.

[yahelordie]

+10