00:02
In this problem, we'll start by doing the matrix multiplication.
00:06
So we take this first row, or in other words, the entire first matrix, and we multiply by the first column.
00:16
And so that means we do 3 times 10, which is 30, plus 5 times 3, which is 15, plus 7 times 2, which is 14.
00:26
And adding those together, looks like it gets us 59.
00:30
Now we take the next row.
00:38
So we do three times nine, which is 27, 5 times 14, which is 70, and then 7 times 5, which is 35.
00:49
And adding those together gets us 132.
00:54
And finally, we take our third column.
00:58
So we do three times eight, which is 24, five times six, which is 30, and then add to that seven times seven, 49 and together that would get us 103 and so now we want to interpret what this matrix represents.
01:17
Now let's think about what we did.
01:20
When we multiplied the three, for example, by the 10, what we're doing is we're taking $3 per hammer and then we're multiplying it by those 10 hammers sold in store a.
01:34
And so that multiplication would tell us how much money store a makes in hammers...