Q36. - Algebra 2

Question

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

 

36. Write a matrix that represents the cost of admissions for residents and a matrix that represents the cost of admission for non-residents.

Step-by-Step Solution

Answer

The matrix representing the data for males and females are:

$\begin{array}{l}\text{ Residents}\\ A=\begin{array}{c}\text{Before 6:00 P.M.}\\ \text{After 6:00 P.M.}\end{array}\left[\begin{array}{cc}3& 4.50\\ 2& 3.50\end{array}\right]\end{array}$ and $\begin{array}{l}\text{ Non-Residents}\\ B=\begin{array}{c}\text{Before 6:00 P.M.}\\ \text{After 6:00 P.M.}\end{array}\left[\begin{array}{cc}4.50& 6.75\\ 3& 5.25\end{array}\right]\end{array}$

Step 1 - 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.

Step 2 - Write the matrix depicting cost of admissions for residents

The data in the table can be organized in two matrices. Let the first matrix representing the cost of admissions for residents be A. Then, 

$\begin{array}{l}\text{ Residents}\\ A=\begin{array}{c}\text{Before 6:00 P.M.}\\ \text{After 6:00 P.M.}\end{array}\left[\begin{array}{cc}3& 4.50\\ 2& 3.50\end{array}\right]\end{array}$

Step 3 - Write the matrix depicting cost of admissions for non-residents

Let the matrix representing the cost of admissions for non-residents be B. Then,

$\begin{array}{l}\text{ Non-Residents}\\ B=\begin{array}{c}\text{Before 6:00 P.M.}\\ \text{After 6:00 P.M.}\end{array}\left[\begin{array}{cc}4.50& 6.75\\ 3& 5.25\end{array}\right]\end{array}$