X= 2 1 2 1 3 2 2 1 4 3 2 1 where the rows represent breakfast, lunch, and dinner, and the columns represent the number of exchanges for each of the four food groups at each meal; Y= 5 0 7 0 10 1 0 15 2 10 12 8 where the rows represent the four food groups, and the columns represent the amount of fat, carbohydrates, and protein per exchange of each food group; and Z= 8 4 5 where the rows represent fat, carbohydrates, and protein, and the column represents calories per exchange. (a) Find the product matrix XY. What do the entries of this matrix represent? (b) Find the product matrix YZ. What do the entries represent? (c) Find the products 1XY2Z and X1YZ2 and verify that they are equal. What do the entries represent

X= 2 1 2 1 3 2 2 1 4 3 2 1 where the rows represent breakfast, lunch, and dinner, and the columns represent the number of exchanges for each of the four food groups at each meal; Y= 5 0 7 0 10 1 0 15 2 10 12 8 where the rows represent the four food groups, and the columns represent the amount of fat, carbohydrates, and protein per exchange of each food group; and Z= 8 4 5 where the rows represent fat, carbohydrates, and protein, and the column represents calories per exchange. (a) Find the product matrix XY. What do the entries of this matrix represent? (b) Find the product matrix YZ. What do the entries represent? (c) Find the products 1XY2Z and X1YZ2 and verify that they are equal. What do the entries represent

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.1: Systems Of Equations

Problem 20E

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Question

2	1	2	1
3	2	2	1
4	3	2	1

where the rows represent breakfast, lunch, and dinner, and the
columns represent the number of exchanges for each of the four
food groups at each meal;

5	0	7
0	10	1
0	15	2
10	12	8

where the rows represent the four food groups, and the columns
represent the amount of fat, carbohydrates, and protein per
exchange of each food group; and

where the rows represent fat, carbohydrates, and protein, and
the column represents calories per exchange.

(a) Find the product matrix XY. What do the entries of this matrix represent?

(b) Find the product matrix YZ. What do the entries represent?

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