Aprofessor bases semester grades on four 100-point items: homework, quizzes, a midterm exam, and a final exam. students may choose one of the three schemes, scheme i, scheme ii and scheme iii, where • scheme i: hw 10%, quiz 10%, midterm 30% and finalterm 50%; • scheme ii: hw 10%, quiz 20%, midterm 30% and finalterm 40%; • scheme iii: hw 15%, quiz 15%, midterm 35% and finalterm 35%. 1. find the matrix which gives the link between these three schemes and these four different kind of examinations. 2. using a multiplication between two matrices, determine the most advantageous weighting scheme for a student who earned 97