Math 240 (J. Wu) Homework #7 due Friday March 5 (by 3pm)
In Kreyszig, 7.9-7.10
To be covered next week: 7.10-7.12
Do all core problems in 7.9, 7.10
7.9 # 8,16,21
7.10 # 20,24,25
In # 20 you can use Maple to compute the characteristic polynomial and
its roots since this is a little messy by hand.
- You can again do this part of the assignment as a study group.
But each person should attach a copy of the solutions to the assignment
they hand in since otherwise the grading becomes too time consuming.
- Read about the commands in the Maple Manual that hepl you cpmpute
eigenvalues and eigenvectors and look at
the Demos on the Web.
- Do 7.10 # 18 and # 20 in Maple. "Take apart" the answers so you list
the eigenvalues and eigenvectors in a form where they would be easy to
use for other computations.
- Show that for an nxn matrix A, the constant term in the characteristic
polynomial is det(A)
and that the coefficient of t(n-1) is, up to sign, trace(A)
defined to be the sum of the diagonal entries in A)
- Show that det(A) is the product of all the eigenvalues, counted with
multiplicity, and that trace(A) is the sum of all the eigenvalues.