be a 3-D space over a field
and consider linear operators
whose matrices relative to
I have been asked to find these vectors so that the matrices of
with respect to
are stricly upper triangular.
My inital procedure was to first find a common eigenvector for
and take that as
, but I couldn't find a common eigenvector that worked, when I calculated
, the respective matrices for
were not stricly upper triangular. I then tried
but that didn't work. Any help would greatly appreciated.