Three professors teaching the same course have entirely different grading policies. The percentage of students given each grade by the professors is summarized in the following matrix:

(a) The point values of the grades are A = 4, B = 3, C = 2, D = 1, and F = 0. Use matrix multiplication to determine the average grade given by each professor.
(b) Professor I has 240 students, professor II has 120 students, and professor III has 40 students. Use matrix multiplication to determine the numbers of As, Bs, Cs, Ds, and Fs given.

Grade D 25 35 30 10 A Prof. I Prof. II 10 20 40 20 10 5 10 20 40 25 Prof. III