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Get Full Access to Linear Algebra And Its Applications - 5 Edition - Chapter 1.10 - Problem 1e
Get Full Access to Linear Algebra And Its Applications - 5 Edition - Chapter 1.10 - Problem 1e

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The container of a breakfast cereal usually lists the

ISBN: 9780321982384 49

Solution for problem 1E Chapter 1.10

Linear Algebra and Its Applications | 5th Edition

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Problem 1E

Problem 1E

The container of a breakfast cereal usually lists the number of calories and the amounts of protein, carbohydrate, and fat contained in one serving of the cereal. The amounts for two common cereals are given below. Suppose a mixture of these two cereals is to be prepared that contains exactly 295 calories, 9 g of protein, 48 g of carbohydrate, and 8 g of fat.

a. Set up a vector equation for this problem. Include a statement of what the variables in your equation represent.

b. Write an equivalent matrix equation, and then determine if the desired mixture of the two cereals can be prepared.

Step-by-Step Solution:

Solution:

Step 1 of 1

a.

Let the number of servings of  General Mills Cheerios be

Let the number of servings of Quaker 100% Natural Cereals be
.

Now,

b. We have  .

The equivalent matrix equation for this will be :

To solve we reduce the augmented matrix for this equation, we get

Performing the row operation , we get

Performing the row operation , we get

Performing the row operation , we get

Interchanging row , we get

Performing the row operation , we get

Performing the row operation , we get

Multiplying row by a constant ,we get

Performing the row operation
, we get

Performing the row operation
, we get

This gives us
and .

Yes, the desired mixture can be prepared by taking
servings of General Mills Cheerios and 1 serving of Quaker 100% Natural Cereals.

Step 2 of 1

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