In this video we will talk about what all are all possible cases of eigenvalues and eigenvectors when we have a system of First order Linear Homogeneous differential equations with constant coefficients. Cases are: 1. When both the eigenvalues are distinct. 2. When both the eigenvalues are same and number of eigenvectors are also same in number. 3. When both the eigenvalues are same but number of eigenvectors is only 1. Then the question arises how to find another linearly independent solution to the given system. Here comes the entry of generalized eigenvectors, which comes from the theory of Jordan Canonical forms. Here I will be stating the formulas for the same. ========================== Link for previous lecutre which is related to the theory of system of First order differential equations:: https://www.youtube.com/watch?v=Y5f6TYmUDds