When you accidentally multiply matrices the way, but nobody notices (Reddit r/mathmemes)
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- Äas pĆidĂĄn 4. 07. 2024
- Matrix multiplication is quite complicated but sometimes we could multiply them entry by entry. Of course, this does not work for all the matrices but only for the well-designed ones!
This meme is from Reddit r/mathmemes
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New mechanic just dropped!! 196-182*0.5=7!! Most Redditors didn't get this!
czcams.com/video/AQiGPtbZo0I/video.html
double factorial
Holy hell
If you're gonna use the double factorial like that then you might as well define the the double factorial of "dropped" and the factorial of "this" lol
Dude. You got my best friend to write math textbook called you can do calculus. thank you.
Please solve integral of (xĂ·dx)
You "broke" the pattern with a green pen. Black and Red alone were expected. We entered another dimension/world? Thank you for the video.
theres been videos where hes used like 4 different pens like in his all in one calc question
@@orangeoranges-mw2sb I never suggested that this is the only instance. But having not seen all of his videos, this did break what appeared to be a pattern. It's also implied in the name.
this feels like when they made i = sqrt(-1)
@@johnchestnut5340 his name is already broken because we normally donât refer to markers as pens. When he first started making videos he used a doc camera (or iPhone?) pointed at his paper notebook and used actual black and red pens on the paper. But the whiteboard videos are the best. He should get a bigger whiteboard - or make a huge chalkboard set up like his friend Michael Penn.
@@stephenbeck7222 You can argue that pens are not markers and vice versa. I can argue that electric cells are not batteries unless configured together into battery. Neither is pertinent to my comment. But you have been heard.
These are the math equivalent of Dad Jokes.
Love that "oldie but a goodie" simplification of 16 / 64.
It works for diagonal matrices because of all the zeros. If it works for anything else itâs a happy accident.
For some triangular matrices because you only have to handle the nondiagonal coefficients too
Bprp helped me so much by teaching me calculus and now he is teaching matrices? Huge W
same.
we started doing limits rn, theyre super easy for me thanks to this channel
@@hmmm6200 my high school became easy asf because of our master bprp, I've seen basically everything in this channel, he made me love math, I am forever Grateful to bprp
I love these "wrong way but not really" rules
bro wrote a book called you can do calculus
In the beginning he goes "ok, so let's discuss what's going on" and i initially thought he was saying "ok, so that's disgusting" and really i agree
r/mathmemes mentioned đ„đ„
Are we stupid?
And is Jessica welcome here?
@@maximilianarold women not welcomed
When you accidentally write the title of the video wrong, but nobody notices
Iâm self teaching linear algebra and this video is super simple and clear to understand! I would love to see more linear algebra videos!
I recommend watching 3Blue1Brown's "Essence of linear algebra" playlist
It's actually product...
hadamard product also known as element-wise product
Euler-Gauss-Euclid-Archimedes-Leibniz-Newton-Ptolemy-Mascheroni-Shanks-Noether product
obviously the EULER(-farey) product, with EULER written in 96 point, and farey optionally written in 1 point.
You joke, but it is, and it has valid uses.
â@@minratos6215 I see you are a man of good taste ... I prefer the Kronecker product.
Tomorrow is my exam i was studying matrix and determinants this notification pop up
Looks like a tini-mini 6th grader tried to attempt this logically đđ
Oh gawd, I never thought others might actually multiply matrices like that. Then I realized, others probably hate matrix math that they will try to get the answer with tricks.
Thank you for teaching me how to multiply matricies! I tried it with some random numbers, and it worked!
There's nothing wrong with multiplying the same elements in each matrix. You just get a different result than the dot product....
I always hated how matrix multiplication is taught. Rows times columns errrggh.. what? Where have I been, did I make a mistake? I always get confused. So I have devised a better method. I imagine the matrices are rotated 45 degrees to right and the result matrix is like a lego brick down between them. That determines its size. Then I imagine the numbers are like balls in a tivoli machine, just waiting to fall down to their place, just block by some imaginary obstacle. Then I release both of the obstacles at once and from both sides numbers start falling in their respecive line. And the numbers that hit each other are the ones that multiply and all the numbers that hit in the same place are added and the result is the number in that place. And then I just rotate the resulting matrix 45 degrees left and put it where math teacher wants it. I don't know if I explained it right so you can imagine it, but this is what I do in my head to prevent myself from making mistakes so I don't have to think in terms of confusing rows and columns.
There is also a way to do the same thing without the 45 degree rotation, if you just imagine the right matrix is just above the left matrix but just to the right, so the resulting matrix is just right of the first and just below the second and the multiplied vectors are basically just intersections..., but the gravity thing kinda helps me...
I guess I better make a video. :D Maybe one day
My linear algebra teacher did the same thing but without rotating. You just raise the second one up above and the resulting matrix fits in between them.
Later, when I set up matrix multiplication for people who hadn't taken this particular course, I found out that this was not standard.
If you really like blocks like that, you would love Kronecker product of matrices. Haha.
The best way to think about it is that you sell apples. In the first matrix rows correspond to different days of selling and columns are the numbers of different kind of apples that were sold. Column in another matrix tells us the prices of those different kind of apples and the result of multiplication is the amount of money you get for every single day of selling. And if we have multiple columns in the second matrix, then it's just hypothetical scenarios where you set different prices for your apples ;)
I feel like you are the Ethan Hunt of MATHEMATICS
I wish I didnât need more of this, but I really do
I didnât get how this was wrong because I was multiplying the correct way and got the same answer. Then I saw the calculation you tried in the beginning.
Thank you
Thank you for helping me on calculus 2
That'd be the Hadamard's which is just fineâŠ
Given that the answer is correct, why would you assume the person who generated it used the wrong method?
When it said "multiply matrices the wrong way" I did thought they meant column times row it got the right answer. Never even occured to me to lazy-multiply the entries.
doesnt matter which video, lambert w functions sure to show up
7:56 "that's not a b it's a six" I appreciate so much that someone else experiences the deep personal horror of "whoops that letter/number/word writing sucked let me fix it" *draws literaly EXACTLY the same fucked up shape as before*
Looked at the thumbnail and multiplied it the correct way and did not understand what's wrong with it... Did not even occurred to me to do it that way đ
sir rubberd the whole 7 just to cross it
So if this and if that, then this. Got it. Thank you for sharing.
just a reminder to watch the vampire matrix stand up maths video
Yeah this post was cool. If we equate the formulas we get b1*c2 = 0 and c1*b2 = 0. Then our other equations inform our other required zeros.
For b1 = 0:
c1 = 0:
(a1 or b2 = 0) & (d1 or c2 = 0)
b2 = 0:
c1[a2 - c2] + c2d1 = 0
For c2 = 0:
c1 = 0:
b1[d2 - b2] + b2a1 = 0
b2 = 0:
(c1 or a2 = 0) & (b1 or d2 = 0)
We were given that c1, c2 = 0.
So 6(2-4) + 4*3 = 0, which is true, which is why the post fulfills the reqs.
Similarly for b1, b2 = 0:
c1[a2 - c2] + c2d1 = 0
Choose c2, c1, and a2 to be whatever; but then you have to calculate d1.
Say c2 = 1, c1 = 2, a2 = 4.
d1 = -6
X. 0. 4. 0.
2. -6. 1. Y.
Can choose X and Y freely.
Cool... đ
That endin lol
0:50 cursed fraction
Can you get all solutions for a in terms of n in a=n*sqrt(n+sqrt(a))?
đđđđđ.
The gamma function should work here. Upper triangular matrices but very surprizingđ
5:00 since regular multiplication is associative, can we add another 4 equations from multiplying matricies in reverse order (AB = BA = C, C is the wrong way)?
Ok, some of them doesn't matter, but seeng AB=BA would be also invalid in general
can anyone recommend a similar channel like this for other subjects too..
I keep thinking I'm finally going to understand matrices but... nope.
"these aren't the same, but here's the system of equations where they are"
l want to see bprp Solving 2017IMO p3
Element-by-element multiplication honestly feels like the most intuitive type of multiplication;
I always thought that it was a bit weird how you are supposed to do that awkward row-column multiplication.
That row-column multiplication is necessary though, because the resulting matrix has the same effect as the two matrices used to make it. Say you have a rotation matrix A and a scaling matrix B. AB would be rotation then scaling all in one matrix
The idea is that matrices represent linear maps, and multiplication of matrices is then the same thing as composition of the linear maps. if A and B are the matrices of two linears maps a and b and X and Y two column matrices representing two vectors x and y then Y = ABX is just another way to write y=a(b(x)). And this linear map matrix correspondance is the real reason why we bother with matrices at all
Yeah, I realise that the row-column multiplication is the real way to multiply matrices;
it just felt a bit strange to me when I first started doing it.
That said, element-by-element multiplication is of course sometimes a desired form of multiplication as well, like maybe if you have various tables of data and want to perform several individual multiplications at the same time.
It looks like you misspelled numbers with hose underlines
Shift the right matrix up so that the resulting N*M matrix fits in the empty space. Then do dot product between the corresponding row and column vectors for each element in the result. Can't get it wrong accidentally that way.
It's easy to remember to dot the first row with each column on the second matrix. Then you get a number for each of those dot products. The hard part to remember is, do these numbers form a *row* or a *column* of the new matrix? I've never been able to come up with a good way to remember that, other than just memorizing it.
I just noticed the resulting number goes in the intersection of the row and column that made it
@@Greenicegod Nice, thanks!
One could also try to find examples with the dot product in the wrong order, ie. col dot row.
Please explain the integral solved by RON GORDAN I am a huge fan and you explain miraculously đ
This one was fun..
Let X=[(a b), (c d)] & Y=[(e f), (g h)]. Then XY=[(ae bf), (cg dh)] if any of the following cases hold:
Case 1: X=0
Case 2: Y=0
Case 3: a=b=c=0 ⧠g=0
Case 4: b=c=d=0 ⧠f=0
Case 5: b=0 ⧠e=f=g=0
Case 6: c=0 ⧠f=g=h=0
Case 7: XâDiag_2(R) ⧠YâDiag_2(R)
Case 8: X,YâLT_2(R) ⧠cg=ce+dg
Case 9: X,YâUT_2(R) ⧠bf=af+bh
Cases 1 & 2 are obvious. Case 7 reflects the fact that multiplying diagonal matrices is easy, that it's componentwise for the diagonal entries. Cases 3, 4, 5, & 6 are not as obvious, but straightforward to verify. Cases 8 & 9 are interesting for only requiring two entries to be 0, such that both X & Y are upper triangular (or lower triangular) matrices, along with requiring the componentwise multiplication to hold for the entry diagonally opposite the 0 entry.
So, are there an infinite number of matrix pairs where this sort of naive matrix multiplication works, then?
If i am honest I thought that this was gonna be a joke on that because there is two square matrices if the same length he flipped which matrices was in front
Scalar Multiplication vs Matrix Multiplication.
doesnt this method of "multiplication" actually have a name and usage as well? i thought i remembered something really specific you can use this for
Hello there
Just curious, why does he write the matrix multiplication like that? I'm used to writing them down in a square, where the first matrix (X) is written in the bottom left, the second matrix (Y) in the top right and the answer matrix (Z) gets into the bottom right. That way it's visually much easier to see what to multiply. Like this:
|Y
X|Z
(forgive me if this covers stuff you already know)
Because multiplication is symbolically represented in algebra by simple adjacency: eg "ax = y" is multiplying a and x. When you use literal numbers, eg "3âą4 = 12" you need the dot (or Ă) to disambiguate, but otherwise no operator is needed. For matrices, equivalently, the symbols are traditionally uppercase letters, often starting with T for the varying values, eg "AT = U" has three matrices, but while the literal form is the square brackets around the grid of values, it's still as a whole a single value in an algebraic expression.
So the only thing left is: why don't you need a different operator for multiplying matrices than numbers? The confusing answer is that matrices actually are numbers! Just like whole numbers, integers, real numbers and complex numbers are all different structurally but can be treated as numbers by adding and multiplying, following sensible rules you learned in early math classes like "(x + y) + z = x + (y + z)" and "0x = 0", so do matrices (and vectors, quaternions, polynomials, etc. to some degree)
The sets of these rules and what structures and operations follow them is group theory.
what is the cross product?
The cross product is a product of two vectors, that returns a third vector that is mutually perpendicular to both of the vectors. The magnitude of the cross product vector, tells you the product of magnitudes of the two given vectors as well as another factor that measures how "crossed" (i.e. perpendicular) the two source vectors are. That factor, is the sine of the angle between them. The cross product is not commutative like normal multiplication, and produces the direction of its output according to the right hand rule.
An application of the cross product is torque. The radius vector from the pivot point, crossed with the force, tells you the torque that the force applies; i.e. the rotational equivalent concept to a force. By convention, we assign torque in the same direction as a standard right-handed bolt would move parallel to its axis, if you spin it in the direction you apply the torque.
@@carultch Thanks!
This stuff really reminds me of ancient greeks, chinese, and babylonian mathematicians.
Its all very simple logic. But from that simplicity, we get some amazingly complex problems and solutions.
Its really sucks that so much has been lost to history. Look at where we are today with just what we have saved, created, and built upon.
I hope everyone here knows how special it is that we are able to gather here, and talk, and learn, and grow together.
Nothing in mathematics is lost to history. Artworks like writings and statues can be lost, because they are unique, but mathematics is objective. We can discover the exact same principles that have been "lost", if any, and given that we have supercomputers now, it's safe to say that there is nothing in mathematics they knew and we don't.
In fact, we've solved problems Euler and other geniuses couldn't, because of technical limitations. We've advanced fields of theories, like knot theory, that would have been impossible to progress without computers.
So please, spare us from your profound sanctimonies.
@apokalypthoapokalypsys9573
Im sorry but i dont care what nasty things you have to say. So go be miserable alone. There is nothing to gain from talking with you.
@apokalypthoapokalypsys9573 Just curious.
Why do you gotta bring me down like that? Im just trying to be positive. Why be so mean? Sorry i have nothing interesting to say. Im sorry for being me. If i could change i would.
You people make me feel like complete trash. And all i do is try to be positive. I dont understand.
Im sorry for speaking. Im sorry for expressing anything. You guys win. I give up. I thought we were lucky to be here together. But now i know nobody feels that way about me. Im just annoying and useless.
Im sorry. And it wont happen again. You win.
Can you pls do sin(x^2)=2sinx?
If I saw this video in undergrad I would have said âman everyone knows thisâ
But now as a professor we needed AS MANY PEOPLE pointing this out possible. I could make a video EVERYDAY for the rest of my life on how to properly multiply matriciels and I will still have students multiply across on the final⊠you read that correctly⊠THE FINAL. As in after months of explaining, office hours, homework, quizzes, and tests⊠they still mess it up. Thereâs always one or two. đą. Makes me want to quit, man.
Integral: tan^2x Ă· (1+sec^4x ) dx Ű how can you solve or just give me a hint
you might've made some typo or there is something wrong in question if you are trying to find real solution but if you want complex solution just change above tan to sec and add and subtract sec^4 above and separate -1 and then in denominator just separate like a^2 + b^2 in complex numbers then it's just simple process â
@@zero-sl3bn denominator would be (a^2 - b^2i^2)(a^2+b^2i^2)??? Did you mean this expression??
@@zero-sl3bn then try with partial fraction??
@@user-zg8ny5tp4g (sec^2 + i)(sec^2-i) and yup partial fraction by keeping sec^2 common in numerator
@zero-sl3bn but how you can apply partial fraction to secx function, because we sec^2x in the denominator..so it would be (AX+C)Ă· (sec^2x+i) + (BX+D)Ă· (sec^2x -i)... but don't get it how to apply on secx function.
When you do matrix multiplication, you need to also "add" another term so that to assemble the real equations.
Matrix in math is just a system to solve a simultaneous equations.
In other words matrix is just an isolated system made from a bunch of simultaneous equations.
Consider the circle equation.
y(t)=r * sin (t)
x(t)=r* cos (t)
But, this is only true for the first quadrant i.e when x and y is always positive.
Later they find out the equation is
x(t)= x * cos(t) + y * sin(t)
y(t)= x * -sin(t) + y * cos(t)
This is the formula for a clockwise rotation in which the rotation is in the form of a circle.
From here you can isolate the equations in a matrix form.
[ cos(t) sin(t) ] [ x ]
[ -sin(t) cos(t) ] [ y ]
So, if you try to assemble the original equation from a matrix form, you must do "addition" or you won't get the original equations.
you sure about that ?
wow im early
Why do you call it a matrix âmultiplicationâ when in fact it is an arbitrary rigmarole? Why donât you just arbitrarily divide all the numbers while you are at it?
2x3=6 is a multiplication.
What you are doing with those two matrices is not at all a âmultiplicationâ.
It's not arbitrary at all. When you understand what's going on, it's very obviously the most natural way for matrix multiplication to work.
@@benkelly2024 âââ your comment is arbitrary because, since it has no explanation, is neither true nor false. Why is it called a multiplication when in fact there are steps other than a multiplication involved? Why is the rigmarole needed? What facts of reality make all this necessary? If there are indeed reasons why this is necessary, why is calling this a multiplication not arbitrary, when it is quite clear that 2x3 is?
Because it has a lot of properties in common with multiplication. Consider how you'd use matrices to solve the following system of equations:
3*x + 2*y = 14
4*x + 5*y = 28
You'll construct a square matrix of the coefficients, which we call A. You'll construct a column matrix of x & y, which we'll call matrix X. You'll then construct a column matrix of the right hand side constants, which we'll call B. This produces the following matrix equation:
A*X = B
You can see that each entry of matrix A, is multiplied by one of the entries of matrix X, somewhere within this process. And just as you'd solve 3*x = 9 by multiplying by the reciprocal of 3, there's a similar method of solving this matrix equation by multiplying by the "reciprocal" matrix of A.
A*X = B
A^(-1) * A * X = A^(-1) * B
A^(-1) * A = the identity matrix I, by definition. This is analogous to the idea of 1, where it is something you can multiply by anything, and return that same anything.
I * X = A^(-1)*B
An identity matrix multiplied by a column matrix, returns that column matrix. Thus:
X = A^(-1) * B
The hard part is finding the matrix A^(-1). For the 2x2 case where A = [a, b][c, d], the general solution is:
[d, -b]
[-c, a], all divided by (a*d - b*c)
So this example:
A^(-1) =
[5/7, -2/7]
[-4/7, 3/7]
Multiply by the column matrix of [14][35] and get:
X = [2][4]
Which implies x=2 and y=4.
@geekonomist I have pointed out that your confusion is simply the result of ignorance, but I have no interest in educating you. If, now that you are aware of it, you wish to remedy your ignorance, that is up to you. The subject you need to study is called Linear Algebra, and it is usually one of the first subjects taught in a mathematics degree.
@@benkelly2024 I asked ChatGPT. I gave it (along with you) shit for three rounds because it kept things absolutely ridiculously abstract (ie : Matrix A represents a Rotation (!?!) and Matrix B a Scaling (!?!). Then after repeated badgering, it finally yielded a real world example, called sales volume of apples and oranges at different prices in different stores. Funny how just the title alone answers all questions I have, and how NOBODY thinks in terms of apples and oranges when teaching and pontificating in comments. And no, it is not a "multiplication" when you combine the values of a spreadsheet of your prices and volumes of apples and oranges. "Multiplication" is an arbitrarily misnamed - rigmarole.
It most definitely is how we multiply matrices. Its called the Hadamard product and its a universal basis for how modern computer architectures compute all the other matrix products hyper-efficiently. Very disingenuous video.
Hey BPRP I love your vids keep it up, I wanted to ask a question is there a way I can contact you?
This wasnât even the way I thought they multiplied them wrongly. I thought they had transposed the multiplication and it does indeed work that way as well. I have a feeling (but not a proof) that any 2x2 matrix multiplication that abides by your proof will also have this quality of multiplying the same way in all three ways
Just a property of triangle matrics whose application is here just
That "middle point" notation for multiplication is hell to read, just draw an "x" please.
But Ă is for the cross-product.