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Current time:0:00Total duration:4:06

- [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. 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 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. 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. 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. So 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. That 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. I'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. And 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. 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 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? 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.