Solve the following system of differential equations given that 
and 
has eigenvalues 
and 
with eigenvectors 
and 
respectively.
1) The system can be rewritten as a matrix: 
2) The system will have the same number of solutions as eigenvalues and each solution will have the form 
. Therefore, this system has two solutions that by the superposition principle can be added together. 
3) The C constants are determined by solving for the given initial conditions 
and 
. 
This amounts to solving the following system: 
After row reduction we obtain: 
So the final solution is the following: 
and has eigenvalues and with eigenvectors and respectively.. Therefore, this system has two solutions that by the superposition principle can be added together. and .