Comments

• #1a) Students did not need to test other properties, finding ONE counterexample would suffice. (students were testing all the properties, which is unnecessary if a counterexample was found)
• #1b) students did not prove (u,u)=0 IFF u=0. Many students proved one way, but not the other.... they had to since we have an IFF relation.
  many students wrote that 2x^2 + 4y^2 + 4xy >= 0 without any justification.
  they need to show the steps: eg. x^2 + (x^2 + 2y^2)^2 >= 0 since each term is >= 0 (we have each term squared).
• 1.c) many students show that (u,u)>=0 but not that (u,u)=0 iff u=0(vector).
• 3.a) many students treated the scalar as if it were in the real field, and not the complex field.
• 5.) I think 2 students got 10/10 for having both parts. Many others had either the wrong conclusion (no such function exists) or only had an example of a function that was linear over R but not over C (namely a simple conjugate fcn, or L(x,y)=(y,x), or =(x,-y) etc). Many students misunderstood the question, i.e. did not realize that 'both ways' had to be considered.

Marking Scheme

• Problem 1: Mark all three parts a,b,c 5 marks each part,
  total 15 marks
• Problem 2: Text Exercise #8 Mark all three parts a,b,c 3 marks each part,
  total 9 marks
• Problem 3: Mark all three parts a,b,c 3 marks each part,
  total 9 marks
• Problem 5: Give zero marks if only the conclusion is stated. 5 marks for each correct part of the conclusion.
  total 10 marks