Assess learners' understanding of the geometric interpretation of eigenvectors and eigenvalues for linear transformations in 2D and 3D. Tasks include computing eigenpairs for small matrices, explaining eigenvalues as scaling (and sign as reflection) along invariant lines or planes, distinguishing algebraic versus geometric multiplicity, interpreting complex eigenvalues as rotations with scaling, and using diagonalization or spectral decomposition to describe the transformation's action and implications for stability. Problems should combine calculation, geometric description or sketches, and concise explanations linking algebraic results to geometric behavior.