How to organize, add and multiply matrices - Bill Shillito

When you're working on a problem with lots of numbers, as in economics, cryptography or 3D graphics, it helps to organize those numbers into a grid, or matrix. Bill Shillito shows us how to work with matrices, with tips for adding, subtracting and multiplying (but not dividing!).

Lesson by Bill Shillito, animation by The Leading Sheep Studios.

[mridulabiswasroy]

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.

[digaddog]

"Once you undertale matrices, you can do pretty much anything."

Its tax evasion time

[hovoag]

thank you very much. i cried when understood this.

[TheMan-cbch]

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.

[gene]

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

[kelseymo]

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

[muffinproject]

"You can't multiply matrices of different sizes."

...20 seconds later...

"Multiply this 10-digit matrix with this 4-digit matrix."

[ObaydFox]

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

[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.

[based_dragon_]

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.

[TMJcafe]

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

[snakeb]

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

[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

[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.

[scottnelson]

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.

[SquidBobCircleJeans]

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

[operatic]

Fantastic video. I'm looking through YouTube 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.

[zitchaden]

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