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.