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).