Using matrices to manipulate data: Pet store

0:00- [Instructor] We're told a certain pet store chain has three types of dog food and each comes in bags of two different sizes. Matrix A represents the store's inventory at location A, where rows are food types and columns are bag sizes. So let's see, it's store A.

0:19That's what matrix A is telling us. They're telling us we have three different types of food, three different types of dog food, and then they each come in two different sizes. So for example, type 1 dog food in size 1, they have five bags of that while type 2 dog food in size 2, they have nine bags of that.

0:41All right. That's fair enough. Matrix B represents the store's inventory at location B. All right, same thing for store B. Matrix C represents how many more, or less, bags of each type and size there are in location A relative to location B. Complete matrix C.

1:03So pause this video and see if you can have a go at that. So we need to fill in the entries here of matrix C. All right, now let's do this together. So let me just review what it just told us. Matrix C represents how many more bags of each type and size there are in location A relative to location B.

1:27So for example, this first entry right over here, we wanna know how many more bags of type 1, size 1 there are in location A than there are in location B? Well, I would take the number that there are in location A and then from that subtract how many there are in location B.

1:47That would tell me how many more I have in location A. So if I take five minus eight, what am I going to get? Well, I'm going to get negative three right over here, and you might already be recognizing what's happening. For every corresponding entry, I'm gonna subtract the entry from matrix B from the entry in matrix A, or another way to think about it is, if I take matrix A and I subtract matrix B, I am going to get matrix C.

2:18I'm just gonna subtract all of the corresponding entries. So if I do seven minus six, and that is going to be one, I'm just gonna color code this. If I do three minus 10, that's going to be negative seven. If I do, I'm running out of colors. If I do nine minus 12, that is also going to be negative three.

2:44And then if I do this brown color, 10 minus five, that is going to be positive five. And then if I do 15 minus nine, that is positive six. So we can see that, for example, type 1, size 2, we have one more in store A than we have in store B. But if we think about type 2, size 1, it shows us that store A has actually seven fewer of that than store B does.

3:17Now we have one last question here that is below the screen, but let me scroll down here. So they tell us that matrix D is defined as follows, or is defines as follows. (chuckles) Make a little grammatical. Is defined as follows: D is equal to A plus B. What does matrix D represent?

3:38So they're not asking us to calculate A plus B. Not asking us to add the matrices, but you know how to do it. You would add the corresponding entries. But what does D represent? Well, if you add the corresponding entries, remember, this is the inventory of store A, this is the inventory of store B.

3:55So if you were to add them, the matrix D would tell you the combined inventories of A and B, for each of the types and sizes.