Assess students' ability to apply the Cayley–Hamilton theorem to reduce powers of 2×2 matrices and derive closed-form expressions for matrix exponentials e^{tA}. Scope: real or complex 2×2 matrices with distinct or repeated eigenvalues (including a 2×2 Jordan block); use the characteristic polynomial to write A^n as a linear combination of I and A, determine coefficient functions (by solving for low powers or using eigendata), and assemble e^{tA} via those coefficient functions; problems emphasize short computations and correct application of the theorem.