Question

For Exercises 36-39, use the following price list for one-day admissions to the community pool.

38. Write a matrix that represents the cost of admission before 6:00 P.M. and a matrix that represents the cost of admission after 6:00 P.M..

Short answer

The matrix representing the data for males and females are:

$\begin{array}{l}\text{Before6:00P.M.}\\ A=\begin{array}{c}\text{Residents}\\ \text{Non-Residents}\end{array}\left[\begin{array}{cc}3& 4.50\\ 4.50& 6.75\end{array}\right]\end{array}$and$\begin{array}{l}\text{After6:00P.M.}\\ B=\begin{array}{c}\text{Residents}\\ \text{Non-Residents}\end{array}\left[\begin{array}{cc}2& 3.50\\ 3& 5.25\end{array}\right]\end{array}$

Step-by-step solution

- Define the concept of organizing data in matrix

A matrix is a rectangular array of variables or constants in horizontal rows and vertical columns, usually enclosed in brackets. Data is organized in such a way that each position has a purpose. Each value of the matrix is called an element.

- Write the matrix depicting cost of admissions before 6:00 P.M

Let the first matrix representing the cost of admissions before 6:00 P.M be A. Then,

$\begin{array}{l}\text{Before6:00P.M.}\\ A=\begin{array}{c}\text{Residents}\\ \text{Non-Residents}\end{array}\left[\begin{array}{cc}3& 4.50\\ 4.50& 6.75\end{array}\right]\end{array}$

- Write the matrix depicting cost of admissions after 6:00 P.M

Let the matrix representing the cost of admissions after 6:00 P.M be B. Then,

$\begin{array}{l}\text{After6:00P.M.}\\ B=\begin{array}{c}\text{Residents}\\ \text{Non-Residents}\end{array}\left[\begin{array}{cc}2& 3.50\\ 3& 5.25\end{array}\right]\end{array}$