Q. 83 - Precalculus Enhanced with Graphing Utilities

Question

College Tuition Nikki and Joe take classes at a community college, LCCC, and a local university, SIUE. The number of credit hours taken and the cost per credit hour (2009–2010

academic year, tuition only) are as follows:

(a) Write a matrix A for the credit hours taken by each student and a matrix B for the cost per credit hour.

(b) Compute AB and interpret the results.

Step-by-Step Solution

Answer

(a) $A=\left[\begin{array}{cc}6& 9\\ 3& 12\end{array}\right] and B=\left[\begin{array}{c}80\\ 277.80\end{array}\right]$

(b)  $AB=\left[\begin{array}{c}2980.2\\ 3573.6\end{array}\right]$

Step 1. Given information

Nikki and joe takes classes at LCCC $6 and 3$ with cost per credit hour $\$80.00$

Nikki and joe takes classes at SIUE $9 and 12$ with cost per credit hour $\$277.80$

Step 2. (a) Write a matrix A for the credit hours taken by each student and a matrix B for the cost per credit hour.

Credit hours taken by each student can be written in the matrix form 

$A=\left[\begin{array}{cc}6& 9\\ 3& 12\end{array}\right]$

Cost per Credit  hour can be written in the matrix form 

$B=\left[\begin{array}{c}80\\ 277.80\end{array}\right]$

Step 3. (b) Compute AB and interpret the results.

We calculate the matrix AB by multiplaying the two matrices

$$\begin{gathered} AB=\left[\begin{array}{cc}6& 9\\ 3& 12\end{array}\right]\left[\begin{array}{c}80\\ 277.80\end{array}\right] \\ =\left[\begin{array}{c}6\left(80\right)+9(277.80)\\ 3\left(80\right)+12(277.80)\end{array}\right] \\ =\left[\begin{array}{c}480+2500.2\\ 240+3333.6\end{array}\right] \\ = \left[\begin{array}{c}2980.2\\ 3573.6\end{array}\right] \end{gathered}$$