► My Precalculus course: https://www.kristakingmath.com/precalculus-course
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
Music by Joakim Karud: http://soundcloud.com/joakimkarud
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // http://www.kristakingmath.com
● ● ● CONNECT WITH KRISTA ● ● ●
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?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com
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