M 311 Spring 2004 HOMEWORK SUMMARY REPORT Chapter number: 4 Section number: 1 Exercise number: 7 Number of papers received: 2 Reviewing committee: Iota List all participating committee members: Clark, DenBleyker Author(s) of paper(s) chosen for publication: ... Comments: We recommend [...]'s solution for publication. We feel that his conclusions were clearly explained and correct, and that no revisions are necessary. The other response was incorrect. It stated that the theorem does not hold for the set of zero vectors. This set of vectors can be expressed in an infinite number of ways, which means it is independent. This is the contrapositive of the theorem, and it holds true, thus, the theorem also must be true. INSTRUCTOR'S COMMENT: Both solutions missed the point of the problem, which is that the CONVERSE part of the proof (at top of p. 155) uses Theorem 1, which does not apply (or even make sense) for a set consisting of only one vector (as is noted on p. 153). Nevertheless, the theorem is true for the set {0}, since both sides of the logical equation are false (the set is dependent, and 0 can be expressed in many ways as a multiple of itself).