Question

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

39. Find the matrix that represents the difference in cost if a child or adult goes to pool after 6:00 P.M.

Short answer

The matrix that represents the difference in cost if a child or adult goes to pool after 6:00 P.M. is $\left[\begin{array}{cc}1& \text{1}\\ 1.50& \text{1.50}\end{array}\right]$.

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.

- Subtract corresponding elements

The data in the table is organized in two matrices A and B. In order to find the difference in cost if a child or adult goes to pool after 6:00 P.M. subtract matrix B from matrix A by subtracting corresponding elements of both the matrices.

$\begin{array}{c}\begin{array}{cc}\text{Before6:00PM}& \text{After6:00PM}\end{array}\\ A-B=\left[\begin{array}{cc}3& 4.50\\ 4.50& 6.75\end{array}\right]-\left[\begin{array}{cc}2& 3.50\\ 3& 5.25\end{array}\right]\\ =\left[\begin{array}{cc}3-2& 4.50-3.50\\ 4.50-3& 6.75-5.25\end{array}\right]\end{array}$

- Simplify the matrix

Further simplify the matrix.

$\begin{array}{c}A-B=\left[\begin{array}{cc}3-2& 4.50-3.50\\ 4.50-3& 6.75-5.25\end{array}\right]\\ =\left[\begin{array}{cc}1& \text{1}\\ 1.50& \text{1.50}\end{array}\right]\end{array}$

In the matrix obtained, 1 dollar representsthe difference in cost if a resident child goes to pool after 6:00 P.M. Similarly, 1.50 dollar represents thethe difference in cost if a non-resident child goes to pool after 6:00 P.M

Here, in second column of the matrix, 1 dollar represents the difference in cost if a resident adult goes to pool after 6:00 P.M. Similarly, 1.50 dollar represents the the difference in cost if a non-resident adult goes to pool after 6:00 P.M