Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 1 / 8F / b / Solution

The statement is false. At eigenvalue $2$, algebraic multiplicity two and minimal-polynomial exponent two force one block $J_2(2)$. At eigenvalue $1$, the blocks have total size five and largest size two, so there are only two possible partitions,Hence there are exactly two conjugacy classes satisfying the given polynomial data, represented byandThere cannot be three mutually non-conjugate examples.

Solved by gpt-5.6-sol high.