MATH 3200-001: ELEMENTARY DIFFERENTIAL EQUATIONS
Fall 1997, University of Colorado Denver
Instructor: Prof. Andrew V. Knyazev

Test 3

Find the most complete answer.

1. Find a number of independent arbitrary constants in the solution using the operator method for the following system

   

   1. 0
   2. 1
   3. 2
   4. 4
   5. None
2. Rewrite the following system in operator notation

   

   1. 

   2. 

   3. 

   4. 

   5. None
3. Find all eigenvalues of the matrix

   

   1. 1,2,5
   2. 1,1,-5
   3. 1,-2,-5
   4. 1,-2,-2
   5. None
4. Find such number c that

   

   is an eigenvector of the matrix

   

   1. 0
   2. 1
   3. 2
   4. -2
   5. None
5. Find linearly dependent vectors:

   1. 

   2. 

   3. 

   4. 

   5. None
6. Find a general solution of the system

   

   1. 
   2. 
   3. 
   4. 
   5. None
7. Find a general solution of the system

   

   1. 
   2. 
   3. 
   4. 
   5. None
8. Which form of a particular solution should be used for the system

   

   1. 
   2. 
   3. 
   4. 
   5. None