Test students' ability to analyze diagonalizability of 3×3 matrices by examining eigenvalues and their algebraic and geometric multiplicities; classify all possible Jordan canonical forms (over C), determine minimal polynomials, and justify Jordan block structure in cases where geometric multiplicity is less than algebraic multiplicity. Tasks may include computing eigenvectors, deciding diagonalizability, constructing the Jordan form for given matrices or parameter families, and explaining implications for similarity and matrix powers.