The characteristic polynomial is , giving
So the algebraic multiplicity . I seem to be getting an incorrect answer for the geometric multiplicity .
By Gaussian Elimination:
It seems to me that we can obtain three linearly independent (LI) eigenvectors from this by setting and to zero in turn. That would give . My textbook however gives (suggesting that we can only obtain one LI vector)
Could you please clarify where I am going wrong in the LI part?