Comments on Assignment 4

1. Students had a lot more difficulty with this one. A few commmon sources of lost marks were for not showing row operations and failing to justify true or false answers. But the largest source of lost marks were the proof type questions. A tip for students is to start off with the algebraic definition of Span or Linear Independence, and go from there.
2. • Question 1: Many students pointed out that if z = 0, then there must be a solution. But they failed to notice that this solution is not unique.
   • Question 4 (True/False): A very common error was to refer to theorem 8, and either reverse the order of implication, or explain why the theorem doesn't apply. The former is simply incorrect, the latter doesn't answer the question.
   • Questions 7, 8 (Span, Linear Independence proofs): Very poorly done; only a small handful of students did the proofs correctly.
3. • - For T/F, some students didn't explain their answers
   • - Also for T/F, students are applying theorem 8 in the reverse order
   • - For page 71 #6, many students said that the last row of zeros implied a free variable
   • - For page 71 #10 (b), a common error was concluding that h=-6
   • - Most students could not prove the results of #7 and #8