How do you multiply matrices?

In this video we’re talking about everything you need to know about matrix multiplication. We’ll start simple and look at what it means to multiply a matrix by a scalar, and then move on to multiplying matrices together using the dot product, and a special trick for remembering how to do matrix multiplication.

We’ll cover rules of algebra for matrices, including commutative, associative, and distributive properties, and show that each of these properties applies to matrix multiplication, except for the commutative property.

We’ll talk about matrix dimensions and how to describe a matrix by its rows and columns. We’ll address the fact that not all matrix multiplication is defined, and that you in fact need the number of columns in the first matrix to match the number of rows in the second matrix in order for the multiplication to work at all. You can also use matrix dimensions to figure out the dimensions of the resulting matrix after the multiplication.

Finally, we’ll look at identity matrices and zero matrices, which act like the special numbers 1 and 0 when it comes to matrix multiplication.

0:17 // Multiplying a matrix by a scalar
0:37 // Applying algebra to matrices
0:44 // Matrix multiplication is not commutative
1:21 // Associative property and distributive property with matrices
2:00 // Matrix dimensions
2:21 // Which matrices can be multiplied together?
2:55 // How to figure out whether matrices can be multiplied together. How to figure out the dimensions of the resulting matrix.
3:40 // How to multiply matrices using the dot product
4:26 // How to remember what to put where
5:16 // Identity matrices
5:51 // Multiplying by the identity matrix is like multiplying by 1
6:31 // Multiplicative inverses
6:56 // Zero matrices
7:23 // Summary

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[Jerkwaad]

I love the way you did this, by inserting/pulling the papers for showing the results. Very comprehensive. You should do more matrix related videos. You are definitely my favorite math teacher on Youtube!

[Chillibiy]

Just needed a brief refresher of matrix algebra, this is spot on!! Thanks for the video. Brief and to the point.

[billreeves]

Watching your videos on YouTube has become a daily thing for me, Krista. I really enjoy your work!

[rahulfederer]

You are a goddamn legend. Thank you so much. Bought 4 courses on Udemy for an exam two weeks later. It's been amazing so far.

[ChrisBradel]

I love your video style. It's readable and visually interesting!

[arkitektbmw]

Awesome timing! Just happen to be going through these. Love my professor, but the way he explained it, I just wasn't getting it. So, Thank you!

[robertchay]

at 2:50, the matrix on the right has 3 rows, not 2

[FadhlyHamzah]

You really put a huge effort on ur channel. Amazing.

[Darkev]

Amazing vid, thanks! Refreshed what i took in high school!

[joecast]

All of ur videos r so good, u make some of the best if not the best math videos on youtube, just wanted to thank-you for how much you've helped me with my math classes. Thanks!

[Ridgerunner]

Great job on this video Krista. I'm taking linear algebra now, and found this video helpful. Keep up the great work!

[picknikbasket]

Haven't done these for ages, fun! thanks Krista

[gavendb]

as an engineer working, it's nice to have refreshers in long forgotten math!

[updownftw]

hOW IS SHE holding the pen, someone please tell me.

[Carlos-qddq]

There is a mistake at 2:48. The first matrix is (2x3) and the second is (3x2). Therefore the multiplication of these matrices IS defined and you get a (2x2) matrix.

[unijvaughn]

Ok but like, how much paper do you have xd very helpful vids btw

[IamJacksColon]

ur cuter than the other youtube mathematicians out there

[gerunkwon]

Her left eye is bigger than her right eye