# Endomorphism/Algebraic and geometric multiplicities/Possibilities/Exercise

Let be a field, and numbers with . Give an example of an -matrix , such that is an eigenvalue for with algebraic multiplicity and geometric multiplicity .

Let ${}K$ be a field, ${}a\in K$ and ${}m,n\in \mathbb {N} _{+}$ numbers with ${}1\leq m\leq n$. Give an example of an ${}n\times n$-matrix ${}M$, such that ${}a$ is an eigenvalue for ${}M$ with algebraic multiplicity ${}n$ and geometric multiplicity ${}m$.