Question

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

37. Find the matrix that represents the additional cost for non-residents.

Short answer

The matrix that represents the additional cost for non-residents is

$\left[\begin{array}{cc}1.50& \text{2.25}\\ 1& \text{1.75}\end{array}\right]$.

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 additional cost for non-residents subtract matrix A from matrix B by subtracting corresponding elements of both the matrices.

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

- Simplify the matrix

Further simplify the matrix.

$\begin{array}{c}B-A=\left[\begin{array}{cc}4.50-3& 6.75-4.50\\ 3-2& 5.25-3.50\end{array}\right]\\ =\left[\begin{array}{cc}1.50& \text{2.25}\\ 1& \text{1.75}\end{array}\right]\end{array}$

In the matrix obtained, 1.50 represents the additional cost a nonresident child has to pay before 6:00 P.M. Similarly, 1 dollar represents the additional cost a nonresident child has to pay after 6:00 P.M.

Here, in second column of the matrix, 2.25 represents the additional cost a nonresident adult has to pay before 6:00 P.M. Similarly, 1.75 dollars represents the additional cost a nonresident adult has to pay after 6:00 P.M.