Find eigenvalues of A = [[4,1],[2,3]]. Characteristic equation: det(A − λI) = 0 |4−λ, 1; 2, 3−λ| = (4−λ)(3−λ) − 2 = λ² − 7λ + 10 = 0 λ = 5 or λ = 2. Eigenvector for λ=5: (A−5I)v=0 → −x + y = 0 → v = [1,1]ᵀ.