Chapter 11.2, Problem 53E

### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

Chapter
Section

### Algebra and Trigonometry (MindTap ...

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

# APPLICATIONSEducation and Income A women’s group takes a survey to determine the education and income of its members. Matrix A summarizes the proportions of members in various categories of years of postsecondary education and income. Matrix B shows the total number of members in each income category.(a) Calculate the product matrix A B .(b) Interpret the entries of the matrix A B . Income level Less than$50,000$50,000to 100,000 $100,000or more None1 to 4More than 4 [ 0.75 0.10 0 0.25 0.70 0.70 0 0.20 0.30 ] = A Totals Less than$50,000$50,000 to 100,000$100,000 or more [ 4 20 10 ] = B

To determine

(a)

To find:

The product matrix AB.

Explanation

Given:

A women’s group takes a survey to determine the education and income of its members. Matrix A summarizes the proportions of members in various categories of years of postsecondary education and income. Matrix B shows the total number of members in each income category.

The matrices A and B are given below.

 Income level Less than$50, 000$50, 000to 100, 000 $100, 000or more None1 to 4More than 4 [0.750.1000.250.700.7000.200.30] =A Totals Less than$50, 000$50, 000 to 100, 000$100, 000 or more [42010]=B

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 AB and the given matrices A=[0

To determine

(b)

To find:

The interpretation of the product matrix AB.

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