Q11. - Algebra 2

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.

Step-by-Step Solution

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 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 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, 

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

Step 3 - Write the matrix depicting data for females

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

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