Comments Assignment 2

• 3.1 b) A lot of students were proving it is 1-1 using the definition of 1-1. This is OK, but takes a lot of time. Instead they can just say that since Ker L = 0, then L is 1-1 By a theorem in the textbook. Few students actually did it that way.
  c) same as above, students were proving/disproving it is onto using the definition of onto. They could have just used an argument saying that since 4 > 3 then it is impossible to be onto. (obviously a bit more explanation is required but the general idea is there).
• On question 3.1(c), for example, the majority of the students disproved the onto property by finding an inconsistency in the system. Even in 3.2(b), there were some students who did not use the fact that ker L is {0} to prove one-to-one, despite having used the theorem in two of the previous questions.
  Also, on 3.1(a), some students only showed that the homogeneous matrix had the trivial solution - failing to show that this is the only solution or that the dimension of the null space is zero.
• After marking the assignmets I found the following systemic errors:
  Problem 3.1 c) - many students didn't know how to prove this.
  Problem 3.2 b) - majority of students said {1,t} was the basis for range L
  Problem 4 - several students just didn't attempt 4

Marking Scheme

Total for Assignment : 44 marks
Problem 1: Text Exercise #26:
    Mark both parts a. and b   5 marks each part,             total 10 marks

Problem 3.1:
    Mark all three parts a,b,c  4 marks part a                total 8 marks
                                2 marks each for parts b,c

Problem 3.2:
     Mark both parts a,b      4 marks each                     total 8 marks

Problem 4:                                                     total 10 marks
            Give 5 marks for getting and working with 
             the equivalent 'matrix' system.
            The rest of the marks are divided among
              finding the general solution correctly and
              expressing it properly using matrices.