MATH 3200-002: ELEMENTARY DIFFERENTIAL EQUATIONS
Fall 1996, University of Colorado at Denver
Instructor: Prof. Andrew V. Knyazev
Test 3

Find the most complete answer.

1. Find a general solution using the operator method

   

   1. 
   2. 
   3. 
   4. Solution does not exist
   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 {-2, 2, 3 } are all eigenvalues of the matrix

   

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

   1. 

   2. 

   3. 

   4. 

   5. None
6. Write the following equation as a first-order system in operator notation

   

   1. 

   2. 

   3. 

   4. 

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

   

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

   

   1. 
   2. 
   3. 
   4. 
   5. None