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).