Chapter 12.1, Problem 24PPE

To determine

To find: the greatest numerical increase in students participating between 2005 and 2010 by using matrices.

Answer to Problem 24PPE

519.

Explanation of Solution

Given:

The weekly sales record below show the number of different colors and models of shoes in two weeks:

Shoe sales, Feb 2-8
color	Model 73	Model 84
Black	153	79
White	241	116
Blue	58	32
Brown	95	47

Shoe sales, Feb 9-15
color	Model 73	Model 84
Black	172	82
White	278	130
Blue	65	29
Brown	103	54

Calculation:

Using matrices to organize the information.

First convert the Feb. 2-8 table into a matrix

  $\left[\begin{array}{l}15379\\ 241116\\ 5832\\ 9547\end{array}\right]$

Then convert the Feb. 9-15 table into a matrix

  $\left[\begin{array}{l}17282\\ 278130\\ 6529\\ 10354\end{array}\right]$

Now, add the matrices,

  $\left[\begin{array}{l}15379\\ 241116\\ 5832\\ 9547\end{array}\right]+\left[\begin{array}{l}17282\\ 278130\\ 6529\\ 10354\end{array}\right]=\left[\begin{array}{l}325161\\ 519246\\ 12361\\ 198101\end{array}\right]$

Now, find the largest number and which color and number shoe it corresponds to 519.