Chapter 8.3, Problem 63PE

Tire final grade in a particular course is determined by grades on the midterm and final. The grades for five students and the two grading systems are modeled by the following matrices. Call the first matrix A and the second R.

$\begin{array}{l}\text{Midterm}\text{Final}\\ \begin{array}{l}\text{Student 1}\hfill \\ \text{Student 2}\hfill \\ \text{Student 3}\hfill \\ \text{Student 4}\hfill \\ \text{Student 5}\hfill \end{array}\left[\begin{array}{ll}\text{76}\hfill & \text{92}\hfill \\ \text{74}\hfill & \text{84}\hfill \\ \text{94}\hfill & \text{86}\hfill \\ \text{84}\hfill & \text{62}\hfill \\ \text{58}\hfill & \text{80}\hfill \end{array}\right]\\ \text{System}\text{System}\\ 12\\ \begin{array}{l}\text{Midterm}\hfill \\ \text{Final}\hfill \end{array}\left[\begin{array}{ll}0.5\hfill & 0.3\hfill \\ 0.5\hfill & 07\hfill \end{array}\right]\end{array}$

a. Describe the grading system that is represented by matrix R.

b. Compute the matrix AB and assign each of the five students a final course grade first using system 1 and then using system. 2 $2.(89.5-100-A\mathrm{.79.5}-89.4)=B.69.5-79.4=C\mathrm{.59.5}-69.4=D.\text{below59}\text{.5=}F$