Solutions Manual to accompany An Introduction to Numerical Methods and Analysis, 3rd Edition

CHAPTER 8APPROXIMATE SOLUTION OF THE ALGEBRAIC EIGENVALUE PROBLEM

8.1 EIGENVALUE REVIEW

Exercises:

1. For each matrix below, find the characteristic polynomial and the eigenvalues by a hand calculation. For some of the exercises, the correct eigenvalues are given, to four decimal places, so you can check your work.

   1. 

      for which ;

      Solution: .

   2. 

      for which ;

      Solution: .

   3. 

      for which ;

      Solution: .

   4. 

      for which ;

      Solution: .
2. Prove that similar matrices have identical eigenvalues and related ...