Rec 1 | MIT 18.085 Computational Science and Engineering I, Fall 2008

[@-steady-8215]

"This is a grown-up course, you are here to learn it, my job is not to force it, it is to help it" Welcome to MIT

[@dydx3741]

my eyes got wet in last 3-4mins ...don't know why i'm so much grateful to know existence of such professor and his teachings.... really bow to your knowledge __/\__ thank you

[@freeeagle6074]

Me too. Just moved by those fabulous professors God gave us.

[@Upgradezz]

Loaded with intuition. The best thing I love about professor is that he thinks with the student as if he himself was learning. That's brilliant and should be the norm. God bless you Dear.

[@ThisiwycfZhung]

Very kind and friendly feelings~

[@matheuscardoso1]

This is amazing... I'm quarantined right now, mesmerized by the beauty of linear algebra. Thank you, Professor.

[@moisessena1307]

Simm

[@PattersAvalon]

Awesome, I'm very thankful to the MIT OCW team for publishing and to Professor Strang for his superb teaching skills, live long and in good health sir.

[@frivolas]

The last 10 seconds of this video are gold. Pure gold. Thanks, professor Strang!

[@Musicantrix]

The mit ocw 18.06 sc is so great... Prof Strang is a real master of the art

[@noelk.5310]

Prof. Strang, you are brilliant teacher! Massive props and many thanks for sharing your great knowledge.... What a special treat, this is extreme helpful. I haven't done maths since days of dinosaurs when I graduated from college. My math skills are rusted. This course helped me to quickly recap the theorems/concepts of systems of linear equations which I need to understand for applying in machine learning models and algorithms (ML course which I am also taking in parallel). Cheers!

[@freeeagle6074]

Same here. Long time dry of maths, but this wonderful professor helped me to easily grasp the key ideas in the maths.

[@actnow4ever445]

Gilbert Sir!! You are a great professor... The way you teach, guiding us step by step, is amazing... Just amazing... I had so many difficulties approaching this subject and now with your help, it all has started making sense. Thank you so much for making your lectures available so easily :)

[@manuelsanchez8259]

I wish I had professors like Gilbert Strang in my University, he excels at teaching!

[@zeffii]

i could listen to Gilbert talk all day long :) Thanks MIT!

[@AnanyaPandeyIndia]

I am amazed how Gilbert develops this intuition mixed with thinking during the lecture. He invokes you to think logically and solve it so that you understand it completely.

[@charlesity]

Woooow! What a great guy. I totally love your way of teaching.... Thank you Prof. Gilbert Strang

[@SphereofTime]

8:21 linear combination is output for maxtrix multiplication

[@SphereofTime]

10:05 result is combination of columns

[@SphereofTime]

11:08 Ax=b. Matrix*number=vector

[@pranshumahajan537]

The way u presented was like totally magical.... and yes they say rightly you dont just give lecture... you create art

[@adarshraj6721]

@47:00 was a great intuition. Never thought we can use transpose in such a way.

[@martinnester]

At 41:20, Dr. Strang points out that for the vectors (u,v,w) when you add up the components of one it equals 0, therefore all their combinations will add up to zero. But this is only the case for when x1=x2=x3. Also this confuses me because when doing matrix multiplication to a vector the columns’ components don’t get added this way. The one example he has does say x =[c,c,c], but that doesn’t cover all the vectors in the subspace of Cx=b. If anyone can help me understand my confusion better, that would be much appreciated.

[@Crasshopperrr]

44:30 Well - _lines_ are not subspaces, only lines through the origin. Ditto with planes through the origin.

[@olz6928]

The fact that the difference of squares are the odd numbers really amazed me. I then realised that we can let x be any whole number. Then the difference of squares is (x+1)^2-x^2=x^2+2x+1-x^2=2x+1. This is the definition of an odd number.

[@biswabismitabag9017]

Very good initiative by MIT.. thanks... From India

[@NolanRuble]

Thanks for the knowledge Mr. Rodgers

[@Crasshopperrr]

25:00 What if the underlying field were circular rather than straight? For example let the underlying field be F_3 = Z mod 2. Then b=(1,1,1) for example would solve to x=(0,1,2) OR (1,2,0) OR (2,0,1). Unless I am mistaken…

[@jsnadrian]

Around 32:00 - I never considered what a pit of despair 'zero' is. I love how he says "you can never come back!"

[@GiovannaIwishyou]

It is like a black hole :D.

[@julianhaighvan]

just fantastic - thank you Gilbert Strang! Best math teacher.

[@sohamarora1592]

hey how u doing now??

[@BuddyNovinski]

I could have used recitations like this one when I took linear algebra at Penn State (but I won't mention HOW long ago)! I couldn't see the forest for the trees.

[@bbv481]

I took this in university 19 years ago, I was pretty good at it, but I feel like I just REALLY understood it when I watched this man.

[@pannapan5727]

This course is really interesting even for math dummy like me.Legendary!

[@Artex123]

hi, dont know if you are going to reply but i just started this course. Will it give me proper and complete knowledge of linear algebra?

[@pannapan5727]

@@Artex123 Yes, would be very helpful

[@Artex123]

@@pannapan5727 thanks for replying :)

[@pranshumahajan537]

Gilbert Strang Sir.... Thankyou so so so much. You can make students cry out of love for maths

[@DuckQuickly]

Thank you for posting the recitations! So differentiation and integration are like A and A inverse, but the entries are like infinite and continuous?

[@SphereofTime]

41:59 ? Picture of plance, combination of vector, multiplication of vector,

[@SphereofTime]

47:13 ATA : rotation in plane?

[@Exhora]

This classes are just so easy to watch... Thank you very much!

[@SphereofTime]

42:58 vector space is bunch of vector s. Rule is to take linear combinations

[@arushsingh9014]

nice intelligent extrordinary i dont know what to say just awesome

[@whenhen]

If you want to get a basic lecture on linear algebra, mit ocw has that course on their youtube channel

[@unomenah]

Thank you. I'm A very newbie

[@allandogreat]

We love this guy.

[@SphereofTime]

34:30 triangle by 3 columns..Dependent

[@SphereofTime]

6:46 3 vectors in column picture

[@SphereofTime]

7:03 how do i take combinations

[@SphereofTime]

11:02 x1u + x2v +x3w

[@SphereofTime]

30:33

[@SphereofTime]

11:50 A[1 4 9??

[@georgipopov2754]

34:09 Why is it so apparent for him to say that "It goes through the origin of course"

[@SphereofTime]

3:00 Subspace

[@rajanmanitripathi981]

Super explanation Got interested back into linear algebra

[@SphereofTime]

42:48 was ist an untrastrun?

[@AkamiChannel]

Why is this video in the playlist for 1806?

[@mitocw]

From the 18.06SC webpage, "Professor Strang recommends this video from his Computational Science and Engineering I course (18.085) as an overview of the basics of linear algebra." See ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces/an-overview-of-key-ideas/ for context. Best wishes on your studies!

[@TripleMoxy9]

At 14:43, he goes through the solutions for x1, x2 and x3 as b1, b1+b2, b1+b2+b3. I'm not sure how he arrives at those solutions and would be grateful for any help.

[@NisargPatel-mj3li]

You can see that both the matrices are equal i.e. each entry in each row would be equal to corresponding entry in the other matrix. giving x1=b1, x2-x1=b2 & x3-x2=b3. Now you can easily get the values.

The ending (48:14) made me laugh, it was just brilliant.

[@MrAutore]

An interesting way of teaching. I like it.

[@rokscheonandprknuketests9250]

Just great. Please keep doing so

[@Mrs_Ela70]

Is there any solution manual for the reference book? (COMPUTATIONAL SCIENCE AND ENGINEERING- by G.Strang)

[@microndiamondjenkins566]

I don't understand.. at 8:20 or so he is saying to multiply the matrix A by the vector of x's, you take x1 times the first column, x2 by the second and so on, but then when goes to solve it, he takes x1 by the first ROW, not column. what am I missing here??

[@andreww2319]

Not a technical or precise answer, but it is 2 ways to the same thing. That thing being the output vector b - which is the the weighted combination of the input vectors. If you multiply the collective x weights by each of the rows the total effect of each goes into the b output vector - row 1's result at the top, row 2's underneath and row 3's under that. That same output vector can be read off the columns the first column says that the output vector has 1 times x1 in the top row of the output vector and negative 1 times x1 in the second row and 0 times x1 in the third row. You do the same with the other columns ... x2 times zero in the top cell, 1 times x2 in the middle and negative 1 times x2 at the bottom. Do the same steps for x3 and then combine the effects ... you'll see the same result as you saw for the row multiplications (dot products). You just have to keep staring at it!

[@not_ever]

This illustrates what he is saying: math.mit.edu/%7Egs/learningfromdata/dsla1-1.pdf

[@jashanpreetkaur316]

@@not_ever thanks

[@amizadeesimpatia8989]

professor Gil is great!

[@nadred5396]

Grateful for Gilbert Strang but, is anyone else still lost, I tried watching every one of his videos but still can't put the picture together.

[@sky_mec]

at 5:40 why 'u' is in wrong direction... shouldn't it be in other side of x-axis...??

[@DailyQuoter-mt2lg]

Perspective is weird when you're trying to draw in 3d

I came here because my professor just told me stuff AS IS, whereas Gilbert will walk with you the path.

[@Squatchmichael]

Work hard, find a fun research project, and you can for graduate school if it's not too late! There are lots of other good undergrad. schools, too. And cheaper :)

[@bilalahmed-fe5xt]

35:43 (- column 1 - column2 )= column 3. So these vector are actually dependent. So we get a plan not whole space... And detC=0 . So kindly sir consider it...

[@real-investment-banker]

He said the same thing , are you high or what ?

[@paperorpaper]

I want to go to MIT! :)

[@rohitrohra8828]

33 50 . How are u , v, and w- star in same plane and u,v,w not in the same plane. Can please someone explain. Any help will be highly appreciated.

[@dickjazz]

I think he drew the picture wrong. W-star should be drawn back in the board.

[@real-investment-banker]

ya picture is wrong but the essence is correct . w can be written in terms of u and v thereby makin it a dependent one and therefore lying on the same plane . w = -(u+v)

[@xiemins]

quick question: the sum matrix is not symmetric with the difference matrix because in the third row its b1+b2+b3 in the sum but in the difference is only x3-x2. shouldn't it be x3-x2-x1? It might not mean anything but i just found it bugging me.

[@mathforai-j5y]

such a treasure!

[@dr.merlot1532]

7/11 was a part time job. What do you think about this MIT OpenCourseWare? In what course will I learn Linear Algebra on the level of Hoffman and Kunze?

[@yashwanth73337]

In second example,how is the third column dependent on first two? And in first example, what's the reason that they are independent?

[@SpeaksYourWord]

In the second example the vectors lie in the same plane whereas in the first they're not on the same plane. In the first example the vectors cover all combinations of third dimensional space and are therefore independent.

[@AbhishekMishra-jd4bn]

proffesor srang: "Anyone who is living in the real world, needs linear algebra"

[@picosdrivethru]

damn.. yeah I'm pretty lost on the pascal problem of the problem set

[@bedoelsayed6970]

can someone explain 11:15 what squares ?

[@SpeaksYourWord]

1^2 2^2 3^2

[@SphereofTime]

28:30

[@naveenrs7460]

Love you sir!

[@quirkyquester]

thank you very much!

[@hollanderson]

Thank you Prof! :D

[@snowdenfu]

why this video in this list？and it is in 2008, interesting

[@jashangill4191]

Hi I could not understand in second matrix, like why are u v and w in same planes u is in xy plane v is in yz plane w is in xz plane

[@Jgn_It]

Let u be a vector in the xy plane, and let au represent a line in the same plane. Similarly, let v be a vector in the yz -plane, and let bv represent a line in the yz -plane. The combination of u and v forms a plane. To visualize this, consider a cake being cut at an angle: the front, right, and bottom sides correspond to the usual xy , yz -, and xz -planes, respectively. The cut surface represents our new plane. Now, w be a vector in that plane.

[@mohittiwari8934]

Thanks MIT

[@will3330]

Is this First year linear algebra (in gr 12 now)?

[@vardaanbhat6780]

Is the space containing no vectors considered a "null space"?

[@jerrychan3276]

+Vardaan Bhat Null Space refers to the set who contains the whole vectors which are the linear combination of the coeffcient matrix A that make the result be zero. EXAMPLE Given matrix A . For the equation Ax=0. All the x that satisfied the equation create a Null Space of A.Profressor note it as N(A). In other words, null space contains all the vector x.

[@davidlovell729]

No. In a linear system, the null space is the set of all vectors that are mapped, under the linear transformation, onto the zero vector. Because the zero vector ALWAYS maps onto the zero vector in a linear system, then the zero vector is ALWAYS in the null space, so the null space always contains AT LEAST the zero vector. If it contains any other vectors in addition to that, then it contains an infinite number of them, because any linear combination of vectors in the null space is itself in the null space.

[@scorpioinoct]

I am your fan Gilbert Strang

[@magicandmagik]

wow those are some huge chalks

[@audreydaleski1067]

Orthogonal

[@kareem_3atef]

ART

[@MovieMad007]

ergg beyond me!

[@ashraf736]

WOW🆒

[@johnnyllooddte3415]

i want a computer program that can design and optimize a plane by itself or my designs.. i want it to ask.. shall i optimize this design for you... click yes.. WALLLAAAA.. i dont have time for this crappy childish stuff..doc johnny,, im not interested in going back to jr college

[@ronr2030]

Thanks for the input ?

[@samahirrao]

I am sorry but someone has to say this.. This is slower than turtles and snails...even after watching the whole lecture one doesn't get to learn anything new..same old engineering stuff. nothing against the prof., he is surely a respected person.

[@alexandruguja3139]

+Sanghamitra Ahirrao I've never seen this stuff before and it sure as hell helps me a lot :D

[@frivolas]

The last 10 seconds of this video are gold. Pure gold. Thanks, professor Strang!

[@frivolas]

The last 10 seconds of this video are gold. Pure gold. Thanks, professor Strang!