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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

APPLICATIONS

Produce Sales A farmer’s three children, Amy, Beth, and Chad, run three roadside produce stands during the summer months. One weekend they all sell watermelons, yellow squash, and tomatoes. The matrices A and B tabulate the number of pounds of each product sold by each sibling on Saturday and Sunday.

Saturday
Melons Squash Tomatoes
Amy
Beth
Chad
[ 120 50 60 40 25 30 60 30 20 ] = A
Sunday
Melons Squash Tomatoes
Amy
Beth
Chad
[ 100 60 30 35 20 20 60 25 30 ] = B

The Matrix C gives the price per pound (in dollars) for each type of produce that they sell.

Price per pound
Amy
Beth
Chad
[ 0.10 0.50 1.00 ] = C

Perform each of the following matrix operations, and interpret the entries in each result.

(a) A C (b) B C (c) A + B (d) ( A + B ) C

To determine

(a)

To find:

The result of the matrix operation AC and interpret the result.

Explanation

Given:

A farmer’s three children, Amy, Beth, and Chad, run three roadside produce stands during the summer months. One weekend they all sell watermelons, yellow squash, and tomatoes. The matrices A and B tabulate the number of pounds of each product sold by each sibling on Saturday and Sunday.

Saturday
Melons Squash Tomatoes
Amy
Beth
Chad
[1205060402530603020] =A
Sunday
Melons Squash Tomatoes
Amy
Beth
Chad
[1006030352020602530] =B

The Matrix C gives the price per pound (in dollars) for each type of produce that they sell.

Price per pound
Amy
Beth
Chad
[0.100.501.00]=C

Approach:

Two matrices A and B can be multiplied if and only if the number of columns in A is same as the number of rows in B.

If A=[aij] is an m×n matrix and B=[bij] an n×k matrix, then their product is the m×k matrix C=[cij], where cij is the inner product of the ith row of A and the jth column of B.

Calculations:

Consider the matrix operation AC and the given matrices A=[1205060402530603020] and C=[0

To determine

(b)

To find:

The result of the matrix operation BC and interpret the result.

To determine

(c)

To find:

The result of the matrix operation A+B and interpret the result.

To determine

(d)

To find:

The result of the matrix operation (A+B)C and interpret the result.

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Chapter 11 Solutions

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