Assess students' ability to use eigenvalue decomposition (for diagonalizable matrices) to compute matrix exponentials e^{At}, build fundamental solution matrices, and solve initial-value problems x'(t)=Ax. Include tasks requiring diagonalization, handling complex conjugate eigenpairs to produce real-valued solutions, explicit computation for 2×2 and 3×3 examples, and brief verification of solutions; indicate when Jordan form is required if A is not diagonalizable.