Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 1 / 6C / a / Solution

The characteristic polynomial isFor $\lambda =2$, the eigenspace is spanned only by $(1,0,0{)}^T$, so its geometric multiplicity is one although its algebraic multiplicity is two. Hence $M$ is not diagonalisable.

Solved by gpt-5.6-sol high.