M 311                                           Spring 2004
                                                                                
                HOMEWORK SUMMARY REPORT
                                                                                
                                                                                
Chapter number: 8
                                                                                
Section number: 2
                                                                                
Exercise number: 18
                                                                                
Number of papers received: 2
                                                                                
Reviewing committee: Eta
                                                                                
List all participating committee members:
    ..., Amanda Coots
                                                                                
Author(s) of paper(s) chosen for publication:  Michael Shelby
                                                              
Comments: Both papers answered the question correctly and demonstrated a
clear understanding of the mathematical reasoning behind the solution.
Mike's paper was chosen because it was typed and also because the other
author mistakenly used Matrix C from problem 8.2.19.  We do, however,
recommend some optional grammatical revisions.
                                                                                
GRADER'S AND INSTRUCTOR'S COMMENT:  Having both eigenvalues the same does 
not mean a matrix cannot be diagonalized -- consider the trivial case of 
the identity matrix,  When a multiple eigenvalue occurs, it is necessary 
to CHECK whether the number of independent eigenvectors for that 
eigenvalue is as large as the multiplicity.  Mike's last sentence should 
read, "Matrix C's eigenvalues are the same, but there is only one 
independent eigenvector, so it cannot be diagonalized."  The solution on 
the Web makes the same mistake, but a correction is attached:
http://www.math.tamu.edu/~fulling/thomson/Template/Solutions/ch8/8_2_18r.txt  
(so congratulations for not peeking at the answers beforehand).
See also the comments on the related problem Ex. 8.1.24.