Assess students' ability to apply eigenvalue and eigenvector methods to solve constant-coefficient linear systems of ordinary differential equations: compute eigenpairs, construct general solutions for diagonalizable and non-diagonalizable (Jordan) cases, handle real and complex eigenvalues to produce real-valued solutions, use matrix exponentials and fundamental matrices, solve initial-value problems, and interpret stability/qualitative behavior of equilibria for 2×2 and small n×n systems.