Assess learners' understanding of eigenvectors as directions preserved by a linear transformation and eigenvalues as their associated scaling factors (including zero and sign), focusing on geometric interpretation in 2D and 3D: identifying eigendirections and eigenspaces from matrices and sketches, distinguishing algebraic vs geometric multiplicity, explaining effects (stretch, reflection, rotation, shear), and reasoning about diagonalizability and invariant subspaces using visual intuition and simple calculations.