Question

For Exercises 11-13, use the table below that shows high school participation in various sports.

11. Write two matrices that represent these data for males and females.

Short answer

The matrix representing the data for males and females are:

$\begin{array}{l}\text{Males}\\ A=\left[\begin{array}{cc}16763& 549499\\ 14620& 477960\\ 14486& 455305\\ 9041& 321416\\ 5234& 83411\end{array}\right]\end{array}$and$\begin{array}{l}\text{Females}\\ B=\left[\begin{array}{cc}16439& 456873\\ 14545& 405163\\ 12679& 340480\\ 7931& 257586\\ 5450& 133235\end{array}\right]\end{array}$

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 data for males

The data in the table can be organized in two matrices. Let the first matrix representing the data for males be A. Then,

$\begin{array}{l}\text{Males}\\ A=\left[\begin{array}{cc}16763& 549499\\ 14620& 477960\\ 14486& 455305\\ 9041& 321416\\ 5234& 83411\end{array}\right]\end{array}$

- Write the matrix depicting data for females

Let the matrix representing the data for females be B. Then,

$\begin{array}{l}\text{Females}\\ B=\left[\begin{array}{cc}16439& 456873\\ 14545& 405163\\ 12679& 340480\\ 7931& 257586\\ 5450& 133235\end{array}\right]\end{array}$