Question

A hardware store chain sells hammers for $3, flashlights for $5, and lanterns for $7. The store manager tracks the daily purchases at three of the chain's stores in a 3 X 3 matrix. What is the total gross revenue from the flashlights sold at all three stores?

• How can you use matrix multiplication to solve this problem?
• What does the product matrix represent?

Answer 1

I'm thinking of multiplying the 1 by 3 matrix [ 3 5 7 ] by the given matrix.

What do you think? @ChasingMaggie

Answer 2

I don't understand any of it, other than you have to add all of the numbers in the flashlight row then multiply the sum by 5 to get the total.

Answer 3

Yes. That would work for the flashlight total and you could get the totals of the other items in a similar way.

The instructions mentioned using matrices so that is what I was using.

Have you already gotten totals for the H, F, and L items using your technique?

If so, please post them.

I will post the matrix technique, and we'll see if it works, okay?

Answer 4

H=$43
F=$115
L=$56

Answer 5

Wouldn't hammers be 81?

$3* (10 + 9 + 8) = ?

Answer 6

I see that we are looking for flashlight gross sales. But, please check those hammers.

Answer 7

Oops, yes it would be

Answer 8

Do you still agree with this for the flashlights: F=$115

Answer 9

Yes?

Answer 10

Read across the flashlight row (left to right). I think you may be going down (top to bottom) for a particular store.

We're doing (3 + 14 + 6) flashlights times $5. What is that?

Answer 11

I did do the row, not the column. 3+14+6=23 and 23x5=115

Answer 12

Correct. I am the one who went the wrong way.

Answer 13

What does the product matrix represent? Is it just three different products from three different stores?

Answer 14

Something is off with the two matrices I have tried.

Look at this. How should it be changed?

Answer 15

I don't know? It looks right to me

Answer 16

I'm confused. I figured out the first two questions, I just need to know the last question.

Answer 17

I don't see what that matrix product represents. I don't think it is the proper matrix for this problem.

Answer 18

Hold on.

Answer 19

Do you see the flashlight total here?

Answer 20

Yeah, I see 115

Answer 21

Look on the left to right diagonal.

Answer 22

Okay... it's all three totals

Answer 23

I don't think the matrix multiplication is properly set up. I am asking @hartnn to assist. Sorry for the delay.

Answer 24

whats off?
what u did is correct ...
you did [3 5 7] times the matrix ...which is fine

Answer 25

In one of the calculations, the totals of the flashlight sales did not turn up as a component in the product matrix.

Answer 26

you do get 155 in the product matrix C

Answer 27

Yes. So, I guess that is all that the Asker needs to explain.

Answer 28

exactly :)

Answer 29

only the diagonal elements will represent the total gross revenue

Answer 30

Thanks, @hartnn

Answer 31

So what do I have to explain?

Answer 32

How can you use matrix multiplication to solve this problem?
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Answer 33

The 3 by 1 matrix is the total number of hammers, flashlights, and lanterns, respectively sold per store.

Answer 34

The 1 by 3 matrix is the cost per hammer, flashlight, and lantern.

Answer 35

The left to right diagonal of the product matrix gives the total revenue from each item. The center entry, $115, is the total sales of flashlights in the 3 stores.

Answer 36

@ChasingMaggie Forgot to add that this link leads to a cool matrix multiplier.

http://onlinemschool.com/math/assistance/matrix/multiply/