M 311                                           Spring 2004
                                                                                
                HOMEWORK SUMMARY REPORT
                                                                                
                                                                                
Chapter number: 5
                                                                                
Section number: 1
                                                                                
Exercise number: 2
                                                                                
Number of papers received: 3
                                                                                
Reviewing committee: Zeta
                                                                                
List all participating committee members:
    Ashley Pagnotta, Zac Robinson
                                                                                
                                                                                
Author(s) of paper(s) chosen for publication: [Michael Shelby]
                                                                                
                                                                                
                                                                                
Comments: Two of the papers we received were great.  They were easy to
follow and the logic was clear.  We chose [...]'s paper to be published
because she included an example and a few more technical details.  The
third paper we got was very difficult to understand.  We can't even
actually tell if it is correct, although it seems to be.  The writing is
very unclear and the logic is difficult to follow.

INSTRUCTOR'S COMMENT:  I didn't think the chosen paper was correct; it 
seemed to confuse subspaces with particular vectors in those subspaces.  
Michael's argument is correct for finite-dimensional spaces.  However, 
there is a much simpler and more general argument:  We want to prove that 
any subspace that contains the original vectors contains their entire 
span.  But the vectors in the span are linear combinations of the original 
vectors, so by definition of "subspace" they must be there!