Q12. - Algebra 2

Question

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

 

Find the total number of students that participate in each individual sport expressed as a matrix.

Step-by-Step Solution

Answer

$A+B=\begin{array}{c}\text{Basketball}\\ \text{Track and Field}\\ \text{Baseball/Softball}\\ \text{soccer}\\ \text{Swimming and diving}\end{array}\left[\begin{array}{cc}\text{33202}& \text{1006372}\\ \text{29165}& \text{883123}\\ \text{27165}& \text{795785}\\ \text{16972}& \text{579002}\\ \text{10684}& \text{216646}\end{array}\right]$ 

Here, second column of the matrix represent the total number of students participating in each individual sport.

Step 1 - Define concept of matrix addition

If A and B are two matrices of order $m\times n$, then the addition of the two matrices will also yield a matrix of order $m\times n$ wherein each element is the sum of the corresponding elements.

Step 2 - Add corresponding elements

The data in the table is organized in two matrices A and B. Add corresponding elements of both the matrices so as to find the total number of students that participate in each individual sport.

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

Step 3 - Simplify the matrix

Further simplify the matrix.

$\begin{array}{c}A+B=\left[\begin{array}{cc}16763+16439& 549499+456873\\ 14620+14545& 477960+405163\\ 14486+12679& 455305+340480\\ 9041+7931& 321416+257586\\ 5234+5450& 83411+133235\end{array}\right]\\ =\left[\begin{array}{cc}\text{33202}& \text{1006372}\\ \text{29165}& \text{883123}\\ \text{27165}& \text{795785}\\ \text{16972}& \text{579002}\\ \text{10684}& \text{216646}\end{array}\right]\end{array}$

Here, second column of the matrix represent the total number of students participating in different sports that is., 1006372 represent total number of students participating in Basketball. Similarly, total number of students participating in Track and field, Baseball/softball, soccer, and Swimming and diving are 883123, 795785, 579002 and 216646 respectively.