McGraw Hill Glencoe Algebra 2, 2012
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McGraw Hill Glencoe Algebra 2, 2012 View details
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Exercise 37 Page 209

Use a 4* 1 matrix to store the purchase quantities.

$28.56

Practice makes perfect

We are given a 1* 4 matrix containing the price of four items. 2.59& 0.49& 5.25& 3.99 To be able to use matrix multiplication, we need to use a 4* 1 matrix to store the quantities Martin bought. 1 2 4 1 Let's find and interpret the product.

2.59& 0.49& 5.25& 3.99 1 2 4 1
2.59(1)+ 0.49(2)+ 5.25(4)+ 3.99(1)
2.59+ 0.98+ 21.00+ 3.99
28.56

The product is a 1* 1 matrix. The element in this matrix is the sum of products of the elements in the original two matrices.

  • The product 2.59(1) is the product of the price of one gallon of milk and the amount of milk Martin bought. This means that 2.59(1) is the amount Martin spent on milk.
  • Similarly, 0.49(2), 5.25(4), and 3.99(1) are the amounts Martin spent on apples, frozen dinners, and cereal respectively.
  • The sum of these products is the amount Martin spent altogether.

Martin spent $28.56 in the grocery store.

Extra

The order of the matrices in the product is important
Note, that we could have multiplied the two matrices in reversed order.

1 2 4 1 2.59& 0.49& 5.25& 3.99
1(2.59)& 1(0.49)& 1(5.25)& 1(3.99) 2(2.59)& 2(0.49)& 2(5.25)& 2(3.99) 4(2.59)& 4(0.49)& 4(5.25)& 4(3.99) 1(2.59)& 1(0.49)& 1(5.25)& 1(3.99)
2.59& 0.49& 5.25& 3.99 5.18& 0.98& 10.5& 7.98 10.36& 1.96& 21.00& 15.96 2.59& 0.49& 5.25& 3.99

In this case the result is a 4* 4 matrix, which does not have any interpretation relevant to the question.