Problem 3: (8 points) The professor in your widgets and gizmos class is trying to decide between three different grading schemes for computing your final course grade. The schemes are based on homework (HW), quiz grades (Q), midterms (M), and a final exam (F). The three schemes can be described by the following matrix A: HW Q M F Scheme 10.10.10.50.3 Scheme 20.10.10.40.4 Scheme 30.10.10.60.2 Suppose that you have a score of x1 on homework, x2 on quizzes, x3 on midterms, and x4 on the final, with potential final course grades of b1,b2,b3.(a) Write a matrix equation Ax = b to relate your final grades to your scores. (b) Row reduce the corresponding augmented matrix until you reach reduced row echelon form