Chapter 2.5, Problem 47E

STUDENT GRADES The grades of student in a finite mathematics course at a certain university are determined by their performances on homework, quizzes, three $1$-hour exams, and a final exam according to the criteria in the following table:

Final Grades Ranges (%)

$90\le A\le 100$

$80\le B<90$

$70\le C<80$

$60\le D<70$

$0\le F<60$

$$

	Weight
Homework average (HW)	$10\%$
Quizzes average (Q)	$15\%$
Hour-exam average (HE)	$51\%$
Final-exam average (FE)	$24\%$

For simplicity, suppose there are only five students in the class with scores as summarized in the following matrix:

$\begin{array}{l}\text{HW}\text{Q}\text{HE}\text{FE}\\ A=\begin{array}{c}\text{Alice}\\ \text{Ben}\\ \text{Candice}\\ \text{David}\\ \text{Eva}\end{array}\left[\begin{array}{cccc}100& 95& 86& 89\\ 90& 87& 78& 82\\ 95& 91& 88& 92\\ 80& 87& 72& 74\\ 76& 72& 68& 65\end{array}\right]\end{array}$

a. Find a matrix $B$ such that $AB$ gives the final scores of the candidates in the class.

b. What is the grade of each student in the class?