How to organize, add and multiply matrices - Bill Shillito

[@digaddog6099]

"Once you undertale matrices, you can do pretty much anything." Its tax evasion time

[@arvindupadhyay9671]

Nah it's sans time

[@a889fhjsk]

"que megalovania"

[@mridulabiswasroy8013]

Fact: Matrices were used to generate the graphics used in the film The Matrix, where the Matrix created by the architect was also created by Matrices.

[@beeterion9003]

Noice

[@TheMan-cb8ch]

teachers really should just put up a video of somone explaining it to the class in a more efficient manner... seriously. like this guy. He's cool.

[@hovoag5169]

thank you very much. i cried when understood this.

[@hey0639]

ik how it feels😂😂😂

[@melissarainchild]

You too? I though it was only me...feels great...that next door opening up :)

[@faizalrahman6027]

😆

[@edsluteria8392]

Rmg

[@anonymouspuppy]

Hovo AG ok

[@gene546]

please bill, do more on math, your explanations are clear and very efficient, at least I feel that way

[@eominneuniqus4297]

He's mad a song for pump it up 5 years ago lol

[@greatestleviathan2827]

@@eominneuniqus4297 what?

[@scottstensland]

Bill has an entire math topics playlist kzbin.info/aero/PLZzHxk_TPOStgPtqRZ6KzmkUQBQ8TSWVX its incredible

[@muffinproject]

"You can't multiply matrices of different sizes." ...20 seconds later... "Multiply this 10-digit matrix with this 4-digit matrix."

[@Powerxxxdown]

Yeah because in this encoding eg, we can multiply a matrices with number Of columns equals to number of rows of another matrices, irrespective of number of columns.The reverse isn't possible.

[@brycetaylor5646]

He says to multiply, the matrix dimensions have to be the "right size" not the same size. To multiply, the number of columns in the first matrix must equal the number of rows in the second.

[@gc-tq8xy]

The same size rule only applies to addition and subtraction. In musltiplication thats not needed but the no. of rows of the second matrix should b equal to no. of columns of 1st matrix used in multiplication.

[@plagiarisepuppet8841]

Ted Ed is always beneficial for memory revolving

[@kelseymo8823]

So helpful! Ted-Ed should post more math videos. Makes math learning fun, especially that one about the fractals.

[@ObaydFox]

at 3:45, when that gy with a ponytail poped up, is it just me or was that SUPER creepy...

[@rishabhlovesglobe2060]

*you*

[@craigoda4284]

Y

[@BillShillito]

Actually, at 2:51 or so, I said "you can do the same thing to get the other entries." You calculate the other three entries the exact same way you calculated the first one. :) Pay special attention to the colors of the numbers in the video, since they're colored so you can see how they pair up - remember, you multiply each pair, then add the results.

[@TMJcafe]

He makes math seem so......cool....and ......dare I say it... Fun. NEVER thought I would say that. What have you done to me!?!?

[@sarahbell180]

+TMJcafe Math is one of the most beautiful things ever, it just usually isn't taught in the right manner.

[@adriatical9016]

@@sarahbell180 Schools definitely gave mathematics a bad reputation

[@based_dragon_0110]

For anyone wondering how to divide matrices in the comments section: Find the determinant of Matrix A. Use |A| to find the inverse. Multiply the inverse by Matrix B. That's it very simplified but you get the point.

[@BillShillito]

If you ask me matrices are most useful in the high school curriculum as a quick and easy way to solve systems of equations - I can't tell you how useful they were for me when doing basic physics problems with free body diagrams, accelerations, tensions, and whatnot. They're a great way to set up the right equations and leave the number crunching to computers. That being said, it's important to go over the processes of that number crunching so you understand exactly what you're doing.

[@Cyclosx]

If only I had this vid 3 years ago for my Linear Algebra course :) I still enjoyed it though, like almost all vids from Ted

[@operatic9537]

Fantastic video. I'm looking through KZbin for videos with disruptive potential in education and this one certainly qualifies. Mathematics is taught extremely badly in general: almost never visually beyond the earliest stages in school, often without any discussion of its practical applications or the problems it solves. You've solved this problem for matrices.

[@ibrahimlokh]

Hope you share those channels with disruptive potential for education

[@snake1625b]

for the encoding part, how can you multiply that big matrix by the 4X4?

[@walterh2113]

Because The big matrix only has two columns and the small one has two rows so those fit together

[@scottnelson1713]

You could easily do a whole video about how to use 4x4 matrices for 3D computer graphics. It's pretty cool how you can rotate, translate, and scale objects, and amazing how perspective works to make a 3D scene that matches what your eye sees. I spent most of my career doing 3D graphics and the matrix was the heart of making a realistic scene.

[@zionj104]

You can kind of divide matrices, but first, you have to find the inverse of the matrix you want to divide by, then multiply. Here's an analogy: you can't divide by 6; you have to multiply by 1/6. (Note: Taking the inverse of a matrix is not as simple as taking the inverse of all of its entries.)

[@zitchaden]

7 years ago now? This is still the best explanation I've seen 🙏

[@BillShillito]

It's not that the matrices have to be the same size as each other - it's that the number of COLUMNS of the first matrix has to equal the number of ROWS of the second matrix. So, for instance, the first matrix might be 3x4, and the second matrix might be 4x5 - the 4's match up, so the multiplication is valid, and your product will be a 3x5 matrix. Hope this helps!

[@Nidomy]

I know how to do multiplication with matrices, but I don't know why we do it.

[@playerguy2]

+Nidomy the encryption is also kinda useless for sending secure messages as you can't divide. only subtract and add, not too secure.

[@playerguy2]

+Nidomy the encryption is also kinda useless for sending secure messages as you can't divide. only subtract and add, not too secure.

[@Darkenedbyshadows]

+playerguy2 do you mean encryption in general or in the video?

[@jaygatsby6660]

+Nidomy one use is the inverse of matrix.

[@ptyamin6976]

+Michael Floering Thank you ill read those. Ive been trying to find an answer for a long time

[@Donnapericolosa]

It's my first time to watch your videos, I love it 😚

[@SquidBobCircleJeans]

Whatever it is, it motivated me. It changed the course of my life. I am now studying matrices.

[@gabrelas]

this was so helpful! i'm in a course called linear algebra and this is the first clear explanation i've seen about matrix operations!

[@anuragsub]

after watching this video,i was encouraged to go do some matrix problems lol

[@omnikar5]

Me too

[@Arwin_Unbeatable]

in 2013 is studied basic linear algebra and after 9 years, i am again learning linear algebra with the physical representation. Its awesome and hard in the same vector space with two direct subspaces

[@KannanNambiar]

This is the way to teach mathematics. I hope you will make another video telling teachers how you achieved your spectacular animation. I do not see any reason why we cannot teach higher mathematics in this way. A beautiful video indeed.

[@BillShillito]

If you go to the original TED-Ed lesson page - the link is above - there's a section you can click on marked "Dig Deeper." That has a few more of the myriad applications of matrices. Hope that's enough to get you started! :D

[@justinlui]

I just started, Elementary Linear Algebra. This is brilliant! I wish I had learned this method first

[@VGF80]

Btw not only does size matter. the positioing of the matrices is also essential for a matrix multiplication to be feasible. the order of a matrix is given by this notation "a x b" where a and b are integers. The first integer (a in this case) represents row while the second integer (b) represents column A feasible matrix multiplication follows this rule: "a x b b x c" Where a, b and c are *unique* integers. In other words, the column of the first matrix must equal the row of the second matrix. The product matrix will be the row of the first matrix and the colmun of the second. In this case "a x c".

[@NotGettinAny]

This is the First Ted video on something I've studied. This comes up in FP1 at A Level Further Maths. Pretty interesting applications too.

[@tammymiles8240]

Learning this in maths. Very helpful - thank you!

[@diptidas938]

please only make hard mathematical consept into simple like this...truly life changing and most worthy thing in the world.

[@KristianYeager]

Wow, I NEVER thought of that way of multiplying matrices!!

[@Autarch127]

Lol, DM Ashura teaching my whole Algebra II class math. Best thing.

[@eominneuniqus4297]

With DeltaMAX classroom

[@malcolmbryant]

I've been there. Maths seems to go from Mickey Mouse to Einstein in the blink of an eyelid.

[@Lewieeeee]

I'm starting Matrices in my Aerospace Engineering maths module tomorrow! So glad I watched this

[@hamidazayed6007]

2:54 For all the confused ones as me, he just jumped a few steps here : -4×1 = -4 3×0= 0 -4+0 = 0.... And so on

[@Hyraethian]

I had to watch that a few times over because that totally lost me.

[@AbhipshaSahuCoPrezIOFA]

I have matrices next year and I'm glad I have a slight head start now!!

[@ranggayogiswara5148]

Math with animation is always fascinating. Thank you for bring us this video

[@fmaco6799]

Math is so beautiful! Thanks for the inspiration TEDEd!

[@11STANE11]

second key on 4:10 is inverse of the first key if someone is interested u can check it on net. u can do it with this formula is A(matrix) * A^-1 (sign of inverse of matrix A) = E (unit matrix sorce:google translate, has 1 on it's diagonal) so it would be like [8 3] * [a b] = [1 0] 5 2 c d 0 1 so after this u make system like u did with multiplying 8a+3c=1 8b+3d=0 5a+2c=0 5b+2d=1 then u solve those using elemetary transformations and u get a=2,b=-3,c=-5,d=-8

[@mohitthawani6839]

best explanation with good graphics its awesome made matrices easy for me

[@EduardoRidel]

Where was this video when I needed it the most. :'(

[@totesmagotes007]

I suck at math. Took a placement test. Ended up in a advanced finite mathematics course dealing with matrices. Felt proud of myself. Felt confident after I realized it was pretty simple. Then shit got complex. Ended up failing the class. True story.

[@BillShillito]

Also, you (as well as anyone else who has questions) should take a look at the follow-up response I posted. I do a lot more examples on that video. :)

[@name.7463]

I learnt more from this video than from my teacher thank you very much

[@drtt1gg3r1]

nice video. The graphic display definitely helped in understanding and the following of the narrative.

[@K1ngHoward]

The rule for multiplying matrices and seeing if they can be multiplied together is to match the number of columns for the first matrix with the number of rows for the second matrix. ex: 2 by 2 times 2 by 5. matrices are named 2 by 2 because they have 2 rows and 2 columns: 2 by 2. so since the first matrix had 2 columns and the second matrix had 2 rows they are equal and you can continue multiplying.

[@Nextlevelgamer-z8s]

Sara masla hi khatam... / You just nailed it... / سیاپا ہی ختم کر دتا جے

[@LEBANESEMACHINE]

@jayfulf Actually it is. There are two columns in the first Matrix, and two rows in the second. Watch it again and you'll understand what It means.

[@BillShillito]

It's the first thing you said - you move along the rows of the first matrix correspond and the columns of the second matrix. That's actually why I suggest placing them visually as in the video - it makes it easier to keep your place. To find any given entry, the row you need to use will be directly to the left, and the column you need to use will be directly above. Does that help?

[@ssj7gokurpg]

in matrix multiplication order matters you can multiply a [2x2] by [2x5] but not [2x5] by [2x2]. a trick you can use is to look at just the column on the left and the row on the right to see if it is equal. i.e. [a x b] by [c x d] if b equals c you can multiply it.

[@tomhandcock1046]

Why is this method not taught in schools? It is so much easier than assigning a variable to each element and then having to remember a string of variables.

[@TheGildedStar]

Thanks TEDEd, I liked this video and the "multiplication/division" one. Now just work your way up through further algebra into trigonometry and calculus until I can become a mathematics major by watching cartoons.

[@shri03992]

Linear Algebra is pretty awesome, it's my favorite field in all of maths!

[@ricardoaugustovillabustama2206]

Interesting way of memorizing the product of matrixes!!!

[@GregoryCarnegie]

you can also use Taylor series to find functions of matrices, such as exponentials and logarithms

[@victorarnault]

For multiplication, you can reduce the matrix to another matrix, row matrix and column matrix. Then, multiply the row matrix for the column matrix, you will got the result.

[@apastalic]

I remember doing these a few years back, I also remember taking the inverses of matrices...? It would be nice to have a TedEd video to jog my memory :)

[@Mech-X48]

This video is a life saver thank you soo much!

[@youkilledma1211]

this is so effective at teaching

[@Sharnjit7]

amazing video helps me a lot understand matrices

[@Ichiloki]

It's awesome !! It's exactly what I'm learning at school ! So cool

[@AlchemistOfNirnroot]

Consider, Aij x Bjk. Notice how the columns of matrix A are equal to the number of rows in matrix B? That is a necessary condition to multiply matrices; also the resulting matrix has dimensions ik, Aij x Bjk = Cik. Now, draw a matrix to fit ik, then for the ik-th entry compute the dot product of the ith entry of A with the kth entry of B (you should've learned dot products before learning matrices - unless on more advanced courses).

[@TheBelmontClan]

Ah, fascinating, bill and ted's magic squares, excellent!

[@MagiKVarna]

I've always wanted s.o. to explain WHY the rule, e.g. for multiplying matrices, is this (row by column). Quite often we're given a rule without even a basic explanation about it, at least according to my experience. And u have to dig on your own if your learning by heart is limited.. :)

[@Richardscoat83]

I did the math and it makes sense! Thank you for clearing that up.

[@Freigeist20789]

A Matrix is a table of numbers. Or as Wikipedia says: In mathematics, a matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

[@ebooks4all81]

Consider to use the program MATRIX to calculate and verify easy all your matrices of differents size and types (numeric, symbolic, complex numbers and mixed matrices) , linear system and more -> jamarana.com/matrix

[@yashchadda473]

Thank you, but why is matrix multiplication the way it is? If I understand right, are matrices just arrays of numbers?

[@ClemensJason]

thank god they made this 2 days before my math exam

[@AdriA11]

I have Linear Algebra exam on friday, but instead of studying i’m here 😂

[@lanamotaz8903]

I swear this is the first video i understand after alt of videos wow even my teacher failed to make me understand

[@ataraxic89]

That is a bit more complicated. It is done in the case of Matrix f(A,B,C) = A*B=C where B contains unknowns. To find be we take (A^-1)*(C)=B

[@destinytheexperimenter4201]

This was very helpful thank you!!

[@locodude12]

multiplication tip: 2x3 2x2 the numbers in the middle have to match in order to multiply

[@orangegold1]

I'm confused... when you encode you multiply the message matrix by the key? So how do you decode if you can't divide. ?

[@JuanCardona]

Multiply by the inverse of the key 1/(ad-bc) * [d,-b; -c,a]

[@aquinomaryt4543]

this was simple nd easy to follow..thankx

[@freekeefox]

I got about as far as lin algebra. I was never a math major, and that stuff just made my head spin.

[@BrittOlinder]

I am happy to learn how to use matrices, but am unsure where or how I would use them. I wish a little more attention was applied to making this useful.

[@donalain69]

so how do you decode that example at 4.15? he said you cant devide matrices, so...

[@stearin1978]

And how do you remember that n - is the length and m is the height ? while in cartesian system it is x - is the length and y - is the height. (may be matrices should be more organized!?)

[@fareedal-bandar2953]

0:43 "they are all around us, even now in this very room" after that i expected to hear "wake up Neo"

[@shrirammaiya9867]

Inst A divided by B the same as A*(B^-1)? where A, B are matrices and (B^-1) is the inverse of matrix B.

[@FishGeorgia]

HEY BILL ITS GRANT FROM GOVERNORS HONORS PROGRAM I ÑOVE THIS

[@MistressSerenity]

The way I remember it is that the middle two dimensions of the matrices have to be equivalent. So let's say you have a 2x3 matrix and a 3x2 matrix. The columns and rows are both different but because the middle numbers are the same ( 2x[3] and [3]x2 ), this means they can be multiplied. By this same rule, a 5x5 and a 4x5 can not be multiplied even though they have the same column size because in 5x[5] and [4]x5, the middle two numbers are different. Hope this is not confusing you more xD

[@truvelocity]

I know this stuff. Plus the D=x, y, z, and w as well as the short cut with a matrix in four x four.

[@yahooeny]

nice lesson from DR. MR. YIFFURA

[@eominneuniqus4297]

This is Lesson from DM Ashura (with him deltaMAX )

[@Fimwind]

The most practical use of matrices I've got to deal with are linear equations that have multiple variables.

[@TheRadicalTheory]

what software did you use to create this video? great video by the way:)

[@Tupster]

I wouldn't expect somebody to get it on the first try. It would be a good time to use the slider to review it until you see what is happening. Multiplying matrixes is certainly easier than something like long division.

[@tharunreddy3278]

Watching in 2023 but still it's ossum explained and ofcourse that matrix in the room

[@Freigeist20789]

You can but it is a bit more complex ... You maybe know that a/b is equal to a*b^(-1) ....you first need to make matrix^-1 called inversion and then multiply it as shown in the video.

[@wokingimpact]

the number of rows times the number of columns is the same which means they can be multiplied

[@JCryer32]

Yeh thanks for saying what's written essentially word-for-word in the xkcd comic.

[@totesmagotes007]

Very cool story bro. The kinda of story i'll tell my grandkids while staring off into the distance as they yawn in confused boredom wondering what the heck i'm talking about.

[@Richardscoat83]

I may have missed something, but didn't he say that you have to have matrices of the same size in order to multiply them together? How would a 4 number encryptions key be multiplied by 10 number matrix?

[@kevinlind4640]

Saved my grades!

[@imbsalstha]

linear algebra is my favourite

[@ThePowerofYeti]

Thanks for the intresting viseo, but as many times, I would like to not only get the HOW explained, but also the WHY.