1. The problem statement, all variables and given/known data If A is a 6x6 matrix with characteristic polynomial: x^2(x-1)(x-2)^3 what are the possible dimensions of the eigenspaces? 3. The attempt at a solution The solution given is that, for each each eigenspace, the smallest possible dimension is 1 and the largest is the multiplicity of the eigenvalue (the number of times the root of the characteristic polynomial is repeated). So, for the eigenspace corresponding to the eigenvalue 2, the dimension is 1, 2, or 3. I do not understand where this answer comes from. Please come someone help me understand this.