I've been asked to find a 3x3 matrix A such that
2) The eigenvectors of A do not span
I believe the second condition implies that A is not diagonalizable, which means it does not contain a complete set of eigenvectors (I am only aware that nilpotent matrices fall under this category, are there others?) and I know that 1) can be expressed as:
but I cannot figure out how to work this out. Can anyone help?