   Chapter 11.2, Problem 54E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

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

# APPLICATIONSExam Scores A large physics class takes a survey of the number of hours the students slept before an exam and their exam scores. Matrix A summarizes the proportions of students in different categories of exam scores and hours of sleep. Matrix B shows the total number of students in three exam score categories.(a) Calculate the product matrix A B .(b) Interpret the entries of the matrix A B . Exam Score Below60 60 to 80 Above 80 Less than 44 to 7More than 7 [ 0.75 0.20 0.05 0.60 0.30 0.10 0.40 0.30 0.30 ] = A Totals Below 60Below 80Above 80 [ 80 170 40 ] = B

To determine

(a)

To find:

The product matrix AB.

Explanation

Given:

A large physics class takes a survey of the number of hours the students slept before an exam and their exam scores. Matrix A summarizes the proportions of students in different categories of exam scores and hours of sleep. Matrix B shows the total number of students in three exam score categories.

 Exam Score Below60 60 to 80 Above 80 Less than 44 to 7More than 7 [0.750.200.050.600.300.100.400.300.30] =A Totals Below 60Below 80Above 80 =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=[0.750.200.050

To determine

(b)

To find:

The interpretation of the product matrix AB.

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