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  • ocw.mit.edu/courses/mathematic­s/18-06-linear-algebra-spring-­2010/video-lectures/

  • how much do i have to pay to have him as a teacher?

  • @gogogino 40,000 per year, roughly

  • @cammarata123 i wll stay with my own that they are free hahaha

  • what this?

  • Just the video I needed... 2 semester later...

  • I am very happy to see the vidoe The Geometry of Linear Equations.after you give this

  • Steady I Really Like This Video The Geometry of Linear Equations

  • Good, I like that you share this video The Geometry of Linear Equations, I wish success always

  • Nice Video The Geometry of Linear Equations That You Share , So Very Nice Thanks You

  • I Really Like The Video The Geometry of Linear Equations From Your

  • Your Video Is Very Useful Sharing The Geometry of Linear Equations.

  • after i watched this video The Geometry of Linear Equations, my insight is very open because the video is very good to give information

  • "why not take the right combination, what the hell." LOL

  • Thank you MIT! One of the most useful channels on YouTube!

  • you gotta be kiddin me!!!!! i am 8th grade in bulgaria and we are learning this

  • @s0cialnetwork indeed

  • @s0cialnetwork Think of it this way. When it comes to uni's like MIT you get people who have close to zilch knowledge on this stuff.. But their intelligence makes up for it. And second. It goes from easy enough to hard thinking very fast. And finally, explanations are more conceptual as opposed to being more about methods. That requires a significantly more advanced thinking eventually.

  • that teacher is just plain and pure awesomemess

  • I love how he so casually says... Let's take a shot at imagining 9 dimensions.

  • Ini dia Yang Gw cari, Good Video!!

  • Top Video!!

  • Good Video. I like Thus. Thanks MIT For Infomations.

  • Amazing , he has deeper understanding of the whole thing

  • 21:25 What? Four 3-dimensional spaces all living in a 4 dimensional space, with each pair intersecting in a plane, and each pair of planes intersecting in a line, with those lines all intersecting at the point that is the solution to your set of equations? Why would anyone have difficulty visualizing that? I think he just forgot his 4d chalk today. ;-)

  • Amazing lecturer. And I love his big and clear handwriting!

  • i found the problem thanks

  • where sound????

    

  • @zakzak257 Sorry, the audio channels are not balanced. The right channel is louder. Adjust your audio settings accordingly.

  • i learned math from this but then i took an arrow in the knee

  • MITで学んでみたいもんだ。見入ってしまった。

  • Αυτός δεν είναι τίποτα μπροστά στον Φιλιππάκη!

  • -I want to file a complaint against professor Gilbert Strang for sexual harassment.

    -Why?What did he do to you?

    -Nothing yet, but he keeps winking at me all the time!

  • @VrmTrela Its too funny

  • ey bin reich aber einsam

  • Comment removed

  • Hi guys,

    I'm studying electrical engineering in the Technical University of Munich and

    i want to spend one semester in the MIT. The problem is that i don't know any exchange programms offered in my university with the MIT. An other thing, i ve been told that i need to find a Student form MIT who wants to spend one Semester in my university too, so that i can make an excahnge.

    Can you help me or do u have some useful links for exchange programms of the MIT.

    Thanks a lot :)

  • I used to excel at the linear algebra. Then I took an arrow in the knee...

  • thank god for this era, so I can watch MIT courses from the other side of the globe. thank you MIT, thanks you YouTube,Thank you world!

  • How does this compare to calculus 1 difficulty wise?

  • @b0ondockz Basic linear algebra is supposed to be easier than calculus, but it depends on individual factors. Calculus depends on the idea of function and limit, linear algebra is all arithmetic and maybe a little geometry, so conceptually LA is more basic than Calc 1.

  • can someone explain how the x and y in front of the columns were changed to 1 and 2?

  • @b0ondockz

    2x-y=0

    -x + 2y=3

    x = 1

    y = 2

  • @b0ondockz Going from the problem statement to "checking" the already-known solution.

  • The course link is down.

  • @Flyrev The course link had a typo and has been fixed (supposed S05 not F05).

  • I hate how he skips the "big definitions". I've been watching some vids from popular US schools and every teacher is different, sucks! Must be like a lottery if you get a good teacher or not, which matters a lot. Very few of the teachers I've seen are any good, they mostly just stand there and do what pleases them, not the students.

  • my theory is that math teachers are so wierd because they have so much math information in their heads that they go crazy.

  • why is he so wierd

  • @matiasmingo3

    cause he's a genius, just like all other MIT professors. If you go to MIT, you are def a little weird jus like everyone there

  • my mind blown up again. yeah, i've understood the first lecture but i cant imagine more than 3 dimensions. something in a 9 dimensional space... i wonder is there any 4 or upper dimensional space or we just wasting our time for a non-existing imaginary space! actually i dont want to call it imaginary because i cant imagine it. there is no more close word to tell this crab than the word imaginary. please someone explain this to me.

  • @paintlaca There are several theories in physics that theorize that there are more than 3 dimensions, there are theories with 10 spacetime dimensions and with 26 spacetime dimensions

  • @paintlaca -Don't feel alone. No one can visualize greater than 3 physical dimensions. It's a limit to the capability of the human mind. We are finite, fallible beings. I wonder the same thing about multiple dimensions. Maybe that's were the quantum particle go between known states.

  • @paintlaca Whether there are "really" more than 3 dimensions in some physical "space" isn't really important. In application we are interested in non-physical spaces with many dimensions. For instance, how many units of each of several thousand items of inventory a store should order for optimal allocation of warehouse space. That's a problem that can be expressed a a vector problem in a space with thousands of dimensions.  Nobody could picture it geometrically but it's very real.

  • He has the gift of teaching! .. so easy to follow his line of thought. This is so different compared to my old algebrateacher,... geez the chalks should file a restraining order to hold him off the boards ... Clone this MIT teacher!

  • some one help me with this question

    A computer technician charges $75 for a consultation plus $35 per hour write a linear equation in slope intercept form to model each situation.

  • @epicnation360DreamZZ Slope Intercept form is y=mx+b, b is the constant. So b=75. Because regardless of the number of hours the technician works, he always charged $75. M=35, and x=hours. y=35x+75 This is the slope intercept form. So for example if the technician works 3 hours, then it would be y=35(3)+75, which is y=180, so for 3 hours of work the technician will charge you $180.

  • nice lecture

  • Do you guys know if this lecture is on the first day of class?

    So it assumes that you have no prior experience with matrices?

  • very good teacher, explains step by step, here in Brazil we thought it was harder classes.

  • I've watched all these now. To begin with he looked like a turtle without it's shell, but now he looks like Fred Astaire. I'ts amazing what a bit of talent can do for a man. These videos have been invaluable as I struggled through my OU maths correspondence course isolated from any other students here on the Isle of Skye. I don't know what I would have done with out them.

    Thank you.

  • GUYS DEFFO PISSED. dont do math but i fucking glad i dont after watching this even though i could change i found it kinda intresting.

  • This is just too perfect... MIT teachers are fucking godlike.

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  • why can't you just solve for y? i mean, set up a linear equation in the form y=ax+b

  • @AL3Xmotodude solving for 1 variable at a time becomes cumbersome when you have 50 equations and 50 unknowns or 50,000 equations and 50,000 unknowns.

  • when i can't go to bed at night i listen to these lectures until i pass out, just like in my real classes :D

  • Gah.. I'm glad I have my teacher and not this guy.

  • Good teachers are by far more rare than gold

  • @atheistfromaustria 100% true

  • lol! omg! This is awesome!

  • i checked my speaker to see whether its broken.

  • Thank you for making this available free of charge!

  • hey, do any of you guys know the requirements for MIT? As of now, I am in seventh grade & in algebra 1 Honors (skiped 7 grade math) I am also teaching myself Geometry, Algebra 2, Trigonometry, PreCalculus, Calculus 1, Physics 1&2, and chemistry 1.

  • just a question : say i take these courses in college / university and go on to be an engineer, will i ever be using this in real life ? like actually be doing real linear algebra or calculus ? im 16 right now in grade 11

    thx

  • @YEUHNBD You'll use functions that describe real life situations.

  • @YEUHNBD yes and no. you would maybe use 1/10 of what you learn in school ;) but it's quit important to know the origin of what your doing and it will give you more '' out of the box'' thinking.

  • @gusti3k yeah that makes sense thx : )

  • @YEUHNBD I am a Electrical Engineer about to work for NASA. While these math classes do not necessarily get directly used in real-world work, they are incredibly important for understanding the material you will learn in universities.

    Especially if you are going for a Science/Engineering major (you should--they are the most marketable things out there right now by far).

    Personally, I'm working on some statistical digital signal processing right now and need a refresher. I don't regret it.

  • @munkeegutz wow thats great good for you ! is this linear algebra harder then calculus ? and are those the 2 hardest maths that there are ? im hoping to go into something that involves chem, math and physics

  • @YEUHNBD Well linear algebra and calculus are just "different". If you have the capacity to do one, you'll be fine at the other. Differential equations is the hardest math I've studied, but some of my friends say that "complex analysis" is one of the hardest math topics out there. It's a huge field which you are just scratching the surface.

    Study hard! :-)

  • @YEUHNBD As someone who did two measly first year physics classes at uni, in physics your math you will use the most is differential equations. Physics deals with the explanation of different scientific phenomena, most of which deal with rates of change (motion, electricity, etc.) If your differential equations are solid, you'll have a better start than most :)

  • @MrFraktur3 Edit. Btw, doing engineering atm, linear algebra is EXTREMELY important. It is the foundation of computer programs that analyse structures, and whilst being able to perform linear algebra is important, but not exceptional (computers can do them instead once you finish uni), understanding them is very important.

  • @YEUHNBD Linear algebra is not harder than calculus. You get to harder maths when you start going into chaotic systems (non linear differential equations and stuff). It all depends on what you find hard or easy. when i started my BA in engineering i found linear algebra easier tho. When you doing advanced fluid dynamics and stuff i found it hard.

  • @svedishbiker I took linear differential equations in spring of last year, and I'm taking linear algrebra now. I actually think linear algrebra is a little bit more difficult for me because of the sheer amount of language and procedures there are to memorize.

  • @munkeegutz poor NASA....

  • this makes perfect since but i have lost every thing of my memory since collage.

  • whoa, gilbert strang is one of the authors for my ap chem book!

  • Огромное спасибо!

  • I feel stupid watching this cause it's so easy...

  • @TRONhack3r row echelon?

  • with his help ,i feel it's so easy to grasp it .

  • damn I'm stupid :(

  • What the hell I took this course in 7th grade

  • Comment removed

  • perfect

  • Comment removed

  • I can not hear the voice, is there anything wrong with the video?

  • @tankstocks It's actually only on the right channel (in stereo)...

  • The Boston Strang-ler.

  • Hello there. Anyone could tell me where I can find some exercises for linear equations (with results).

    Cheers

  • @MrLlud I hope you have found the exercises for linear equations. Now watch this. "Speed maths- Multiplying without multiplying". Click on my username and check the vid. Cheers.

  • he make it look soooooooooooo easy

  • wow, why wasn't this guy my linear algebra prof in first year....

  • This guys is second to King Khan for the best for teaching linear algebra.

  • I got a 4 (out of 3-5) in Linear Algebra on Chalmers University here in Gothenburg and still I had not understood linear combination as good as with this guy... :P

  • I stumbled upon this lecture and watched the whole lecture. I struggled with this stuff at school but this man made it simple and grasped my attention with his amiable manner and knowledge. Thank you for inspiring me to go back and finish my A level math!

  • Thanks from Brazil professor Strang !

  • It's so cool. I finished one of the technical universities in Europe, and I listened to some good lecturers, but this one is far more better than any of my previous professors.

  • why have one of my speakers broke

  • i love this dude >< he's going straight for the lecturing and i understand him very well :O sweet Job prof ^^ ima stick to your lectures :D find some usefull things i can use in my study :D

  • thanks professor strang

  • he is a good professor...i can understand quickly

  • Why is it that I will not do my Algebra 2 homework but yet sit down and take notes from this brilliant video?

  • Muito bom! Gostei da aula. ^^

  • The subtitles are not timed with the speach. It's a pitty.

  • simple and clear IS what we need to learn math!!! thx Professor!

  • He is telling a story, a story about something called linear algebra

  • My right ear enjoyed this lecture.

  • in Istanbul many of my friends watch this videos. thank you Mr. Strang, you are an amazing professor.

  • @ozenhkn Even other cities of Turkey :P

  • thank you so much  that really helped me allot :) love the professor,

  • An eight dimensional shape in R9! Holy fuck my brain is having a meltdown!

  • This is truly amazing! I love math (especially

    algebra). To have a teacher like this can even make an 14 years old, like me, understand almost everything though my native language is Swedish. That means I first have to translate everything (in my mind) to Swedish and at the same time I have to do the mathematics. Pretty impressive. :)

  • Why is calculus non-linear?

  • Clear and concise explanation. Professor you enlightened me in less than 40 min. I wish I had a math professor like you in college. Thump up to this amazing video :)

  • why cant my math teacher be like u?

  • @tpcardoso

    Thanks to the Internet, anybody willing to upload their lectures to YouTube can be your teacher :-).

    Remember you are your main teacher. Seeking is the basis of acquiring and building knowledge.

  • man... what i would give to have a math professor whose native language is english

  • إنتهيت من هذه المحاضرة كاملة

    I know about soultion of equation systems by the two methods: 1-Row Picture and 2-Coulmn Picture ; the soultion ( if there is one) will be always point of interesection of ( Lines for 2 Dimensional; Planes for more than 2 dimentions) but it point always always

  • This is great stuff. My professor uses the word vector a lot but he never gave us a picture of what a vector is in the context of Linear Algebra. Seems they are excactly the same as the vectors in physics which cleared my mind up quite a lot :)

  • its funny how the first lectures have the most amount of views then it falls by a factor of 1/r^2

  • I learned this in 11th grade.

  • @Maedhrosz Makes sense this is the first class so its the easy stuff.

  • Im 13, hopefully i will understand this when i get to college... if i get to college. Or is this in highschool?

  • @samrudi

    This is the Machussets Institute Technology of UNITED STATES . Let ' s wish you upon REAL ENTRANCE to it when you reach your OFFICIAL AGE .

  • @samrudi this can be taught in highschool classes. my freshman course in highschool just touched base with the matrix aspects, but the row vs. column pictures are just slightly ahead of what I learned. I dont see why this cant be a unit in highschool courses, its pretty simple to follow along.

  • i think that the lecturer missed to wright his x matrix at the first example of 3x3 matrix

    correct? 

  • @mroglow well he didn't really forget it because you will see that the X matrix is not really important later on.

  • Comment removed

  • thanks for the lecture and for subtitiles!

    Greetings from Poland

  • I'm taking this class right now =]

  • @benben829 This is only the first lesson. That's why it seems "introductory". You can save your comment of "didn't meet the high standard" till the final exam.

  • MIT not meeting your high standards? Disappointed in MIT? What do you expect? Math classes are basically the same no matter where you go. This professor is amazing to be able to teach linear algebra in such a simple and straightforward approach. I absolutely hate it when professors don't break it down for students. If anything, it's an ego trip. So with that said, I applaud Prof. Strang for his both brilliance and humility.

  • @Repented I go to UBC and I can tell you I was also surprised when I found that MIT courses are no different from UBC courses at the 1st and 2nd year level. Now, I realize this is to be expected from any top universities. The true value of these lectures I think is that they're online for people who don't have any access to higher education!

  • I agree. I took Linear at a State school in PA and from the looks of it I could have done just as well in this class.

    But Linear was the only Math class I actually enjoyed. I loved learning to do Gaussion's algorithm by hand. It was a puzzle pure and simple.

  • I'm surprised at this lecture. Not that this is a bad lecture in any way; this teacher is brilliant. But rather the level of MIT's courses didn't really meet the high standards it holds.

  • Nice lecture and amazing teacher.

    Still i thought that MIT lessons would be 1000 times harder than that. This is really easy. Maybe it's because it's just the introduction lecture, still i find that pretty disappointing for a school that renowned.

  • Great teachings, thank you very much and greetings from Mexico.

  • how easy is linear algebra when you take the right professor!!

  • is he winking at his students? lol

  • Brilliant professor.....I love how his extremely smart but still humble

  • @andrijja92 knowledge=/=intelligence 

  • He's not only brilliant but has got a sense of humour.

  • Comment removed

  • do we have sound problem in this video?

  • @MrRajesh1983 I think it does but try without headphones, it should sound normal again.

  • you have done nice job by uploading these lecture. nice lectures

  • Thanks, MIT. I can't audit courses at my university without paying full tuition! I just want to learn the stuff, not go bankrupt. Thanks to you I can do the former without doing the latter.

    Keep it up!

  • now THIS is a good show!

    no matter what

  • But linear algebra is easy

  • @CleitonXPS to say things like that.... every topic of maths is easy.. no wait every topic of every subject is easy..

    but to think of it it... only when we understand them so well and get the concepts well embedded we start finding them easy.. and thats what MIT ocw is doing.

  • @CleitonXPS Help me chief!

  • I'm 13 years old, and I understand Professor Strang. Wow! You are an amazing teacher!

  • I have a question. if 8th column is // to 9th column, what will happen? or is it possible that 8th column is // to 9th column?

  • @cliumay9 In the case where the 9th column is equal to the 8th column, you will be limited to 8 dimensions inside of the total 9. Your final 9th column adds no new information. In linear algebra terms, your matrix will fail to span the vector space. In other words, you cannot create the final 9th dimension from just combinations of the 8. Think of it as trying to create z-space when you only have x and y. It's not possible with ONLY x and y.

  • this video clip makes me one step beyond Nobel Prize!!!!

  • This is not the best way to explain the vector. We in Banja Luka we work more generally. Vector is not only directed along, they can also be a polynomial, matrix, function ... We first do algebraic structures (groups, fields, bodies), numbers (real, complex), combinatorics, polynomials, and then vector spaces, matrices, systems of equations and eventually own their own values​and vectors of the matrix ... Our course is much better than this. Come to Banja Luka and teach all: D

  • @Satanailo you are doing it that way because you Serbs are very smart.

  • This is not the best way to explain the vector. We in Banja Luka we work more generally. Vector is not only directed along, they can also be a polynomial, matrix, function ... We first do algebraic structures (groups, fields, bodies), numbers (real, complex), combinatorics, polynomials, and then vector spaces, matrices, systems of equations and eventually own their own values​and vectors of the matrix ... Our course is much better than this. Come to Banja Luka and teach all: D

  • thanks for loading these kind of videos

  • 2x-y = 0

    -3y + 4z = 4

    arent this lines instead of plains??

  • @Santakingkong no, they are planes in 3d. Trust me, try graphing them. standard form for a plane is n_x(x-a)+n_y(y-b)+n_z(z-c)=0. They appear to be lines in 2 dimensions.