Using matrices to manipulate data: Pet store | Matrices | Precalculus | Khan Academy

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, see, it's store A that'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 one dog food in size one, they have five bags of that, while type two dog food in size two, they have nine bags of that. All 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. So 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. 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. So, for example, this first entry right over here, we want to 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. That would tell me how many more I have in location A. So if I take 5 minus 8, what am I going to get? Well, I'm going to get negative 3 right over here. You might already be recognizing what's happening. For every corresponding entry, I'm going to 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'm going to get matrix C. I'm just going to subtract all of the corresponding entries. So if I do 7 minus 6, that is going to be 1. I'm just going to color code this. If I do 3 minus 10, that's going to be negative 7. If I do—I'm running out of colors. If I do 9 minus 12, that is also going to be negative 3.

And then if I do this brown color, 10 minus 5, that is going to be positive 5. And then if I do 15 minus 9, that is positive 6. 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 two size one, it shows us that that store A has actually seven fewer of that than store B does.

Now 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 defines as follows. Make a little grammatical correction; it is defined as follows: D is equal to A plus B. What does matrix D represent?

So 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. So 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.