A range of possibilities for eigenvalues and eigenvectors

How many eigenvalues should we except? How many linearly independent eigenvectors should we expect? What are the possibilities? Does it matter if eigenvalues are repeated? In this video we see a whole bunch of different examples in the 2x2 case. Learning Objectives: 1) Given a matrix, compute the eigenvalues and corresponding eigenvectors. This video is part of a Linear Algebra ourse taught by Dr. Trefor Bazett.