![]() Notice, I took the product, first entry in the row,įirst entry in the column, those two products, then the product of Going to be 2 times negative 1, so 2 times negative 1, plus negative 2, plus negative 2 times 7, plus negative 2 times 7. More real estate here just so I think it will be useful, especially this very first time that we attempt to multiply matrices. Makes no sense to you, I will show you what that actually means. We're going to be taking the dot product of this first row and this first column to get this top leftĮntry right over here. Of the corresponding terms, the product of the first terms, products of the second terms, and then add those together. Vector dot products, this might ring a bell, where you take the product Now what does it mean to take the product of a row and a column? If you are familiar with Product of this row, of that row with thisĬolumn right over here. To get this top leftĮntry right over here, we're going to take the The standard conventionįor multiplying matrices is we're essentially going to take. We added corresponding entries, but that is not the conventionįor multiplying matrices. ![]() Negative 2 times 4, put a negative 8 here. Product right over here, why don't we just multiplyĬorresponding entries? 2 times negative 1 would One convention could have been why don't we just, for our Have the same dimensions, and you just add the correspondingĮntries in the matrices. When you add matrices, both matrices have to You could have thought about multiplying two 2 by 2 matrices. Let's just think about how this could be. Matrix multiplication the way I'm about to Of matrix multiplication, which I'm about to show you, why it has the most applications. Types of phenomena, you'll see why this type I'm going to show you is the way that it is done, and it's done this wayĮspecially as you go into deeper linear algebra classes or you start doing computer graphics or even modeling different I want to stress thatīecause mathematicians could have come up withĪ bunch of different ways to define matrix multiplication. You to is the convention, the mathematical convention for multiplying two matrices like these. What I want to go through in this video, what I want to introduce Let's say it's negative 1, 4, and let's say 7 and negative 6. Matrix right over here that it's also going to be 2 by 2. Let's say that thisįirst one right over here is 2, negative 2, 5,Īnd let's say 5 and 3, and then I have this We have got 2 matrices, and I'll just, for simplicity, I'll start with two 2 by 2 matrices.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |