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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

##### ISBN: 9780321982384

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The container of a breakfast cereal usually lists the