2. Elimination with Matrices.

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: ocw.mit.edu/18-06S05
KZbin Playlist: • MIT 18.06 Linear Algeb...
2. Elimination with Matrices.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

[@PhucLe-qs7nx]

00:00 Lecture overview 02:40 Elimination Success 10:35 Elimination Failure 14:30 Back-substitution 18:55 Elimination matrices 33:00 Matrix multiplication 37:00 Permutation matrix 42:52 Inverse matrix

[@atharrosyad291]

this comment deserves a pin tho

[@nightlessbaron]

@@atharrosyad291 And voila it got one

[@collegewifi5024]

ya i agree phuc le, that dude sucks

[@manilrabia9385]

@@nightlessbaronwhy did your 'voila' sound like David of cs50

[@johnbanwell6391]

Gilbert Strang is a wonderful teacher.

[@Vidrinskas]

At first this guy's style seems awkward and clumsy but then 30 minutes later you realise he's sucked you in completely and totally mesmerised you. Amazing teaching.

[@eevibessite]

kzbin.info/www/bejne/rJ7Wg4KQisyme8U

[@anandsaha01]

1:42 "The idea of elimination ... I mean you would have thought of it .. Gauss thought of it before we did only because he was born earlier which is natural idea .. ahh .. died earlier too" ... ROFL! This prof has a geeky sense of humor ...

[@sreeharipillai9163]

Such a humor ... died earlier too :)

[@bisheshbohora9394]

thug life..😎😎

[@ionbobia]

Someone in the audience added a comment and the teacher, interrupting the idea being expressed, confirmed "...and died earlier too..." No intention for humor here!

[@hovhannisyanani]

@@ionbobia it is intention for humor, because he didn't skip the audience comments... this is called "perfect teaching skills"...

[@vivienne_lavida]

"Maybe I'll leave the author to prove that..." He is the author of the textbook they are using though! Hah!

[@DavidFlores-re5ht]

Vivienne Do i came to the comments to see if anyone noticed this also lol

[@rkus07]

Any one serious about Linear Algebra uses Gilbert Strang. I used it in 1991 on school, sometimes still refer to it. I have also used Calculus by Strang.

[@MayankShrivastava0]

36:24

[@yabinsong3484]

I think what he meant was to leave it to the author of the associative law to prove that the law works.

[@lonehermit2776]

@@rkus07 He has calculus??

[@tolgamulayim3176]

I love how the first lecture had 2+ million views and every other lecture after decreased just like in real life

[@barszrhl445]

tolga boşver sen ne yaptın hepsini izledin mi ?

[@alexc4507]

It’s a real shame too because it’s probably just due to the shitty audio 😞 He is a god!

[@pauljohny200]

@@alexc4507 Another reason is many people are not comfortable with maths ..its hard.. for many ..and then they leave..the quality of lecutre is always good ..They need the mind and desire to complete it .. might be thats not their priority

[@NeuralxAi]

hey Have You Done the Exercises Of this Course??

[@syuann]

Thank you Rabbit he’s not God. He’s definitely one of the best in the world at this though, and his lectures are 100% worth listening to.

[@woodknight3752]

After so many years of using linear algebra, until today I finally understand the meaning of matrix multiplication. matrix*vector is linear combination of the columns of the matrix, and vector*matrix is linear combination of the row of the matrix. Then from this standpoint, the meaning of permutation matrix becomes so obvious. Thank you Prof. Strang.

[@lowgalaxy7232]

老马，没想到在这遇到你了。

[@slohcinana9848]

Oh schnapps 😅 Thanks lol because sometimes we need contents like these😁

[@akash.deblanq]

can someone please explain this to me? I think I am missing this point and thus the permutation matrix is becoming kind of difficult for me.

[@akash.deblanq]

okay, so after 3 days I actually understood the concept. Kind of cried a little bit when I did. I am so grateful to Prof Strang.

[@akash.deblanq]

If anyone is confused about this part, keep watching from 20:00 to 25:00 of the video

[@DanielCoutoF]

This is not a lecture, this is art.

[@NeuralxAi]

hey Have You Done the Exercises Of this Course??

[@pushkarpandey9917]

This comment was discussed in his recent interview...😃😄

[@luxtenebris764]

I saw your comment randomly, than wathan went to vid 0 interview, skip some seconds, the interviewer said your comment , zhit life is so tiny

[@MasterCivilEngineering]

Watch more art here

[@DanielCoutoF]

Ty guys for telling me, the funny thing is i think i already saw this interview and didn't even realize they were talking about my comment, 5 years is a long time i guess.

[@solomonxie5157]

Lecture video timeline Links Lecture 0:0 Elimination pivots and an example 3:9 Failure of Elimination method 10:34 Augmented matrix 14:50 Operations of matrices elimination 19:24 Row operations of Matrices Multiplication 20:22 Column operations of Matrices multiplication 21:43 Elementary Matrix 24:46 Include all elimination steps in one Matrix 33:29

[@yokego9544]

gra

[@aashudwivedi]

I look for your comment in each lecture. You are the hero we need :)

[@Happyflower131]

Thank you sm

[@neerajbhatt700]

Thank my man

[@zappist751]

congrats on marriage lol

[@osmanjant]

I like this professor so much, listening his course is an amusement.

[@JoffreyB]

do you mean he is playing clown role for your entertaining pastime?

[@VictorRodriguez-zp2do]

He's not that good at explaining in my opinion, I had to go and search for everything in this video on internet to actually understand what he was talking about, if I only had this video to learn I would have to struggle a lot in order to understand the lecture.

[@-steady-8215]

@@VictorRodriguez-zp2do people have different mathematical maturity. It's not possible for every course to dumb it down for people like you and me. Not saying they don't start from the ground principles, it's just that they don't spend as much time there as we might need. I learnt some linear algebra in high school so I am able to follow this course by pausing in between. But if this would have been my first introduction to linear algebra, I would have sat there scratching my head and blaming professor strang to be a terrible teacher.

[@mithatcancamur2819]

@@JoffreyB u mad?

[@Jack-lg9mq]

@@VictorRodriguez-zp2do I found these videos great, however, I already have a degree in Maths and used this as a refresher. I would agree that he probably doesn't do a very good job at explaining new concepts so don't be disheartened if you need to read other material - I would have too.

[@shawnwilliams77]

He teaches the way mathematicians do math, lol. It comes to him as he goes along. Such a natural teacher. How I wish I had him...

[@ceidass]

44:16 When you see your ex again

[@robby1992]

you are genius

[@2012vsk]

whats the exact time stamp?? could not get it

[@ceidass]

Its the motion, he sees it, goes like "Bliah" and hides it again :)

[@aryensujjan]

awesome observation

[@radwizard]

hahahah I see what you did there ;)

[@SirNeshorn]

"oh, did I just invent a negative one?" - made me laugh =) Love these lectures, very well explained and at a comfortable pace. Thank you for this.

[@kathyhalton8352]

You should see the 2blue1brown ones :)

[@tcveatch]

I’m pretty sure he did that on purpose to test people’s paying attention or not. If you didn’t notice until the audience said something, you weren’t paying attention. It’s a suggestion to pay closer attention, expressed subtly..

[@diegoferrari3341]

@@tcveatch and about the 5? -2 times 2 minus 1 wouldn,t be -5?

[@pseudolullus]

​@@diegoferrari3341 1-(-4), bro

[@physicsisawesome696]

I was quite proud when I actually noted down -2 instead of -1 and then he corrected himself. Ngl

[@seanpitcher8957]

This is 100 times better than any course I could have paid for. Got his book for 50 bucks, followed along and saved myself a lot of headache and got an awesome reference. No wonder the guys at MIT are geniuses with teachers like this.

[@rivercovey3906]

Is the homework out of his textbook?

[@be2112]

@@rivercovey3906 yes

[@LAnonHubbard]

I've studied linear algebra from another online source, and that's given me a great foundation, but this lecture has really helped me to SEE the matrix multiplication from a higher level. Before this video, I hadn't considered that the left multiplication can be thought of as applying row operations.

[@xiaohanwang3885]

"@35:53 Forget the word 'associative', but don't forget the law". Love this.

[@ChuckEarnest]

That was the point I knew I had come to the right place to learn this.

[@Wahrscheinlichkeit]

Dr. Gilbert Strang is a truly great professor

[@Hataldir]

5 years of physics+4 years of phd in astrophysics and this man managed to give me a much clearer picture of algebra operations than what I got from all my professors. Thank you so much for these lectures Proff. Strang!

[@ekdud2772]

there's something about his lectures that make it so easy for me to concentrate and follow along. I think it's because he thinks out loud; verbalizing the literal thought processes he runs through to compute this stuff, like he himself is learning for the first time and trying to understand what's going on. even though he's on a higher level than all of us mathematically, he still retains such a clear understanding of the basics.

[@antoniomilici7682]

When I was young I studied these topics at high school and again at the first year of the degree in physics 16 years ago. Now I’m rather surprised in be interested and in spending time to watch these valuable lectures on linear algebra, above all because I have nothing to do with them in my current life. But concepts are here so clearly explained that they turn me on the pleasure to remember how I was, that time puzzled, and how you can catch up comprehension of things after so many years.

[@lee_land_y69]

Brilliant. He needs to be recorded. His every sentence clarifies some linear algebra confusion that I had. Even though I have done this corse in my university, I still find it useful to watch his lectures. Even the most introductory ones, like this. Truly amazing job.

[@Erebus2075]

love how many small extra's he throws in constantly, as small "notes" to know ^^ keeps the mind awake and entertained in wonder :D wish my professors was as invested in their lectures :)

[@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

[@MethenySco]

I've never seen math explained so clearly, and so engagingly...He almost held me in suspense waiting for the next step....Brilliant.

[@GREAT-yu4hh]

I'm japanese and an university student. I already learned this kind of things but this proffessor is awsome ! I do hope he is still alive.

[@akashrajput6536]

He is not just the great teacher, but also the great artist. He just teaches these things seamlessly, and this is an art.

[@DharambirPoddar]

This kind of lecture is only possible when your deep passion for your work! Huge Thanks, Sir Strang!

[@hyzy96]

This guy is amazing...When teachers taught this in my college everything went right off the top of my hat...

[@Alperakay2008]

thank you very very much professor Gilbert Strang I'm watching these from Turkey 🇹🇷 ❤

[@RishiSharma2]

The way he is teaching linear algebra by taking example of solving linear equations and not just throwing all the formulas without their incentive is really great.

[@oltasat]

Am here as a Graduate student who is up for a Behavioral economics interview in two weeks and i need some Econometric analysis background led me here as a foundation and am not even mad.. the Professor is just amazing.

[@joshuafancher3111]

Row operations multiply on the left, Column operations multiply on the right. 41:00 - perfect clarification

[@roninkegawa1804]

When you combine those lectures with the ones from 3 Blue 1Brown you get a superb class that opens the doors to mastery. Tank you. I am teching myself math just for the fun of it thanks to You Tube!

[@templar19]

Seeing the concepts of linear algebra intertwined like this is quite amazing! I have tremendous respect for this prof for taking the time to not only prepare these lectures but to put them together into a brilliantly clear and intuitively appealing mathematical tour-de-force.

[@superslash946]

First video series ive watched without getting bored (as for educative videos), this teacher rocks, all hail Mr. old genius guy. Perfectly understandable, my respect to him.

[@francisovenden6993]

He's got such a lovely piece-by-piece, jigsaw-building lecturing style, as if he is rediscovering and rebuilding the knowledge in front of us

[@arbdistress5592]

Having a great teacher is so important! I have known all these operations for over 20 years, but really until now I know what it truly means by matrix multiplication! All my previous teacher just shown me the operations but never explained what it is trying to do.

[@ramenmachinegun]

Glad to see these lectures. It would have been an honour being taught by this professor! A lot of things are making sense today, that didnt make sense when I took college a decade ago.

[@jeffreychan9049]

how many chalkboards are in that classroom? lol

[@melissarainchild]

Never enough... ;)

[@MasterCivilEngineering]

Find here

[@user-ux2gz7sm6z]

LOL IKR

[@victorserras]

I have so much respect for professor Gilbert Strang. He's at such an advanced age in these videos yet he can still give such great lectures. In fact it's 2018 and he still is giving lectures!

[@olgashatunova2385]

The key ideas all in one lecture! Bravo Dr. Gilbert Strang! Love your presentation!

[@TheAInfinity]

853,620 quit already.

[@joss3_py]

2,531,489 *

[@snowpunk116]

'gauss given order' lol

[@snowpunk116]

s29.postimg.org/gygdrho4z/Screen_Shot_2014_02_20_at_3_17_54_PM.jpg?noCache=1392929043

[@OsvaldoCarro]

I like how he deliberately pauses for a second when contemplating a question, not because he is thinking about the answer, but because he wants you to think for yourself for that brief moment before he continues. Brilliant.

[@theroohith]

40:49 That's wonderful way of saying it

[@ivanreii]

"He was born earlier.. it was natural idea.. and died earlier too" xD

[@ionbobia]

Someone in the audience added a comment and the teacher, interrupting the idea being expressed, confirmed "...and died earlier too..." No intention for humor here!

[@DavidBulczak]

I love this lectures. I refresh my math knowledge with them. Thank you!

[@spacecapitalism7152]

It is so beautiful when you finally understand and can figure out those e matrices quickly and put it together into one transformation matrix.

[@pultural]

31:53 - my first "ahaaaaa" moment...so excited to move forward with this course, just brilliant!

[@michalchik]

This guy is a beautiful example of how much value is added to a simple lecture, when teh lecturer knows his subject deeply and apprecaite what it is going to be used for at higher levels. He is doing an excellent job conveying the basics while teaching the students how he thinks. This is going to drive the students that just want to know how to solve the problem nuts, and be a boon in the long run for the really bright and intuitively deep students. I have never seen matrices taught with such love. I say this as a teacher that teaches basic matrix math.

[@thomaselder4076]

This instructor is wonderful.

[@GauravJain108]

Thank you, Professor! Elimination matrix inverses are one thing that I admire about this video. They are so intuitive to construct now.

[@georgesadler7830]

This is a fine lecture on elimination of matrices that I am finally learning for the the first time. DR. Strang, I love the way that you explain matrix multiplication.

[@AmanuelGeda]

I love Prof. Gilbert's lecture videos on Linear Algebra. I read his books and watched his videos five years back, but I enjoy it watching him again.

[@user-gd3uw3dx5p]

it's like i can hear him when i study his book... He is just excelent...

[@MasterCivilEngineering]

Excellent he is dear

[@Os_Bosniak]

▲ Aside from what Professor Strang teaches great, he also has a refined sense of humor. Gauss discovered before us, not only because he lived before us, but also died before us. Well, then, because of the "mistake" in the third row and the second column, when he "promised" A to one of the students at the exam.

[@user-fh1do9xb4n]

God bless you, Dr Strang! I've struggled with matrices and matrices operation since more than a year, and thanks to you I've finally had the 'Aha!' moment.

[@easycooking9882]

I think it would be better for someone who already have linear algebra background. I learned something from another perspective. The meaning behind it. For new learners, it is still hard.

[@black_squall]

Yeah i find him really interesting to listen to but if this were a beginning lesson I would be scratching my head

[@spirit-ph1no]

curtsher11 Then this would not be a good lecture at all. A class is suppose to be taken from a perspective that you are starting to learn. I just started this lecture and I am still unsure if I should continue watching it.

[@black_squall]

***** I'd find something more basic. No sense in stretching your mind on the first class.

[@spirit-ph1no]

+curtsher11 Thats the problem. There are key elements in matrix multiplication that he did not covered. I already learned what they are but if your missing a building block, then you cant study ahead.

[@alina_dial]

+EasyCooking yea ,absolutely ,its not for new learners ,its for the one who really wants to know how all things works ,, and why we should learn them and what is the best way to solve the problems, i do suggest everyone to learn linear algebra once .

[@deepuraveendran1903]

This is the best lecture for Linear Algebra.

[@user-ji6ki8jy8l]

您是我见过的最好的老师，祝您身体健康 You are the best teacher I have ever met. I wish you good health

[@MChanakya]

Thank you, MIT OpenCourseWare and Prof Gilbert Strang. I had never thought of basics of matrices in this more clearer fashion.

[@Muslim604c]

900,000 people did not like the change in sound quality.

[@NeuralxAi]

hey Have You Done the Exercises Of this Course??

[@acco5038]

I don’t need to take linear algebra in college but it’s 3 am and here I am 1 full lecture deep too late to stop now

[@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!

[@HankC9174]

i appreciate how leaders in their field can teach the simple parts with enthusiasm

[@Ehbraham]

I'm too dumb for MIT, but his lectures are so much simpler and easy to understand than my professor's. #SJSU

[@cjhhong]

It is a honor watching this. Thanks

[@davidewing9088]

I love the way this instructor presents this subject!

[@John-lf3xf]

Upto 19:00 Row operation elimination and back substituton(row eschelon form)

[@viq234]

OMG I studied this at uni, but I haven't used maths in a long time. I was trying to figure out how he got a 5. Took me 10 minutes to work out that 1 - - 4 = 5

[@tb100020161]

I was trippin on this hard too. I was thinking -4 - 1 = -5 wtf lol

[@akash.deblanq]

@@tb100020161 same lol

[@MasterCivilEngineering]

Good it worked for u

[@tndoan]

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

[@bayroncastillo7653]

his passion to teach is one of the most beatiful things i have seen it ! wow .. he looks like feymann i mean his way of teach us

[@marinabaskakova2333]

Such an amazing professor, he turns math into a fascinating story! If most teachers at MIT are even 70% that good, that explains how students there get so smart haha

[@alfredomulleretxeberria4239]

They have to be smart and highly disciplined in order to even get in. The difficult part at MIT isn't understanding course material. It's doing homework assignments, tests, projects, and participating in mandatory extracurricular athletics programs.

[@ayushsingh562]

I never Get bored watching these lectures.Prof.Gilbert Strang is awesome!! Thank you Sir :))

[@jackdaniel1579]

I love this guy! You see a lot of passion on him 😊

[@Az9819]

Professor Strange made the subject very very very interesting & challenging. A delight in a troubled world.

[@NessaRojas]

I'm liking these videos a lot, but I admit that if this was my first introduction to Linear Algebra, I would be confused. I have already had a LA course before, and these videos are just great for me to think about things differently and connect the concepts in different ways. Have had a few "aha!" moments with things I only did mechanically before.

[@lee_land_y69]

That’s why reading material is so important for newbies. Most of MIT lectures are difficult without proper prior reading.

[@digitizerSF]

I just caught that: "Keep them in their Gauss-given order" (instead of God-given...hahaha)

[@euclid9492]

This is night and day to my professor. So much simple insight I didn't glean like the simple fact: to swap columns, put the elementary matrix on the right. Wow. I didn't get this until now, I would always try to transpose in a roundabout way.

[@landerhaag3688]

Thank you Gilbert, thank you MIT ❤‍🔥

[@fireblizzard2287]

Thank you so much sir, for uploading this playlist on Linear Algebra. I need those concepts for Quantum Mechanics classes.

[@iamjessehamad]

when the love child of mr rogers and bill nye decides to teach algebra

[@user-bv8wy8cn7o]

Nice lecture. Multiplication of matrices is clear and professor wonderfully explains how to find elimination and inverse matrices. Thank you very much!

[@princeardalan]

This is one of the most beautiful lectures on Gaussian elimination.

[@sadianaputra9794]

he is the best professor i know

[@Newbport849]

26:33 DENIEEEEDDD.

[@emailfilters]

I haven't seen matrices since college. This is the absolute best explanation I've aver seen: clear; methodical; complete! I can't wait 'til Monday (Ooh! I don'e have to: there it is!)

[@parthabanerjee1234]

Dear Professor, Linear algebra is fascinating. I had difficulty understanding Algebra because I could not see beyond the symbols and notations. But I did not realize before that algebra is a symbolic language to express geometric shapes.

[@abhishekshah11]

My teacher's should've taught me this 10 years ago. Imagine where would I be if I knew this way of thinking back then :/

[@doubleja]

"AHHH, sorry he's still there" ^.^

[@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.

[@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.

[@Vmt16]

I have absolutely no idea what he's talking about (I just simply suck at math + I'm not that advanced) but the way he teaches it makes me curious about it and also wish I knew how to do math like that.

[@GreenGodDiary]

Watch lecture one if you havent. If you want to be good at math, you can be, but you need to work hard :)

[@Vmt16]

***** I'm gonna try that sometime, would really be a useful skill.

[@Peter_1986]

Vmt16 If you are unfamiliar with math then I highly recommend KhanAcademy - that site has countless math videos and the site is extremely easy to use. You don't need to be a member or anything, you can just enter the site, then choose "Subjects" at the top of the page and go to "Math" and then just start watching the videos and practicing the example problems - and it's even 100% free! It's a perfect educational site in every possible way you can think of, and the creator of the site, Salman Khan, is also very likeable and relaxed and has a great sense of humour as well. Here is a direct link to the site: www.khanacademy.org/

[@Vmt16]

Laurelindo I'll try that later, thanks for the tip!

[@lwskiner]

Vmt16 This lecture is a mess, it follows no logical path in its explanation of reduction methods, mostly random thoughts . Go to Khan Academy for this portion for clarity and the whys.

[@TheGoldenriff]

Its professor from futurama irl! Haha strang is a living legend.

[@dlwldn915]

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!

[@AllanArtillery13B]

Thank you...I enjoy how Professor Strang reveals the beauty of the subject, step-by-step.

[@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 ;-).

[@ACTlVISION]

"Keep the matrices in their Gauss-given order"

[@MrMechyserra]

Thank you!! These lectures are so clarifying and ease to watch!

[@coolguy9616]

This guy is so wholesome

[@alimemon7611]

No. It should be 5 since we are subtracting row 2 FROM row 3. So i.e 1-(-4) = 5

[@acho8387]

oh... you're THAT guy..

[@ivan-nm1xn]

Thanks! I was wondering about that.

[@AhmedKhashabaa]

Its (row 3) - 2 (row 2) 1 - 2 ( -2 ) = 5

[@jacobramirez5508]

Ok now this is where Im getting cought up on... Its 2x row 2 so you can cancel out the third row because you are subtracting row 3 from row 2... so 2(0 2 -2) - (0 4 1) (0 4 -4) -(0 4 1) =(0 0 -5) so in turn wouldn't matrix U be (1 2 1) (0 2 -2) (0 0 -5)

[@MrSupernova111]

Shahan Memon Thanks!