Linear Algebra: Eigen Everything - Mastery Assessment

This is a comprehensive and challenging quiz designed to test your mastery of eigenvalues, eigenvectors, and their associated concepts. It moves beyond simple calculations to probe deep conceptual understanding of linear transformations, stability, and the geometric meaning behind the algebra. To succeed, you must synthesize information about the characteristic equation, multiplicities, and the conditions for diagonalizability.

Key Formulas:

• The fundamental Eigen-Equation: $A\vec{v} = \lambda\vec{v}$

• The equation for finding eigenvectors: $(A - \lambda I)\vec{v} = \vec{0}$

• The Characteristic Equation for finding eigenvalues: $\det(A - \lambda I) = 0$