The number of “exchanges” for breakfast for each of the  four food groups, respectively, are 2, 1, 2, and 1; for lunch,  3, 2, 2, and 1; and for dinner, 4, 3, 2, and 1. Write a 3*4 matrix using this information. (b)  The amounts of fat, carbohydrates, and protein (in appro-priate units) per exchange in each food group, respectively,  are as follows. Fat: 5, 0, 0, 10 Carbohydrates: 0, 10, 15, 12 Protein: 7, 1, 2, 8 Use this information to write a 4*3 matrix. (c)  There are 8 calories per exchange of fat, 4 calories per ex-change of carbohydrates, and 5 calories per exchange of  protein. Summarize these data in a 3*1 matrix.

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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A dietician prepares a diet specifying the amounts 
a patient should eat of four basic food groups: group I, meats; 
group II, fruits and vegetables; group III, breads and starches; 
group IV, milk products. Amounts are given in “exchanges” 
that represent 1 oz (meat), 1/2 cup (fruits and vegetables), 
1 slice (bread), 8 oz (milk), or other suitable measurements.


(a)  The number of “exchanges” for breakfast for each of the 
four food groups, respectively, are 2, 1, 2, and 1; for lunch, 
3, 2, 2, and 1; and for dinner, 4, 3, 2, and 1. Write a 3*4
matrix using this information.
(b)  The amounts of fat, carbohydrates, and protein (in appro-priate units) per exchange in each food group, respectively, 
are as follows.
Fat: 5, 0, 0, 10
Carbohydrates: 0, 10, 15, 12
Protein: 7, 1, 2, 8
Use this information to write a 4*3 matrix.
(c)  There are 8 calories per exchange of fat, 4 calories per ex-change of carbohydrates, and 5 calories per exchange of 
protein. Summarize these data in a 3*1 matrix.

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