SOLUTION: The following purchase is made at each store: 6 pounds of sugar, 3 cans of peaches, 2 pounds of chicken, and 5 loaves of bread. Use matrix multiplication to find the total bill at

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Question 1202836: The following purchase is made at each store: 6 pounds of sugar, 3 cans of peaches, 2 pounds of chicken, and 5 loaves of bread. Use matrix multiplication to find the total bill at each store. You may use decimal answers for this problem.
Data from three supermarkets is summarized in the matrix below:
Store 1 Store 2 Store 3
Sugar (per pound) [ $0.74 $0.79 $0.83 ]
Peaches (per can) [ $1.32 $1.39 $1.54 ]
Chicken (per pound)[ $3.49 $3.39 $3.29 ]
Bread (per loaf) [ $2.48 $2.59 $2.39 ]

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer:
Store 1: $27.78
Store 2: $28.64
Store 3: $28.13


Explanation:

The goal is to compute this matrix multiplication


The result will be this 1x3 matrix
%28matrix%281%2C3%2Ca%2Cb%2Cc%29%29

To compute the value of 'a', we compute the dot product of the row %28matrix%281%2C4%2C6%2C3%2C2%2C5%29%29 with the first column of the other matrix.
a = 6*0.74 + 3*1.32 + 2*3.49 + 5*2.48
a = 27.78







The value of b is found in a similar fashion, but we dot product the row %28matrix%281%2C4%2C6%2C3%2C2%2C5%29%29 with the second column of the 4x3 matrix.
b = 6*0.79+3*1.39+2*3.39+5*2.59
b = 28.64







I'll skip the steps for calculating c, but this is what the final result looks like

The results then tell us the final bills for each store
Store 1: $27.78
Store 2: $28.64
Store 3: $28.13