Hi,

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?

Thanks.