3/14/2024 0 Comments Matlab matrix times vector![]() ![]() The home stretch now, to get this bottom row second column, or second row, second column, we multiply this row essentially by this column right over here. 5 times negative 1, 5 times negative 1 plus 3 times 7, plus 3 times 7. Second row, first column, second row, first column. Second row of this first matrix, and for this entry, We're now in the second row, so we're going to use the Sometimes matrix multiplication can get a little bit intense. Now let's just power through it together. Out the bottom left entry and the bottom right entry. It's going to be 2 times 4, 2 times 4 plus negative 2, plus negative 2 times negative 6. We're still in the first row but we're in the second column To get this, to get this entry right over here, we're going to take theįirst row from this matrix and the second column from this matrix. This is going to give us some number, and we'll calculate that in a few seconds. Product of the first entry, product of the second entry,Īdded them together to get. Vectors and dot products, don't worry about it. If that doesn't make sense to you, if you're not familiar with That's essentially taking the dot product of this row vector and this column vector. That's right over there, and then I added them together. Second entry in the row, second entry in the column 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 |