def find_eigenvector_2x2(A, eigenvalue):
    a = A[0][0] - eigenvalue
    b = A[0][1]

    if a == 0 and b == 0:
        a = A[1][0]
        b = A[1][1] - eigenvalue

    return np.array([-b, a])


for lam in [1, 3]:
    v = find_eigenvector_2x2(A, lam)
    print(f"Eigenvalue {lam} -> Eigenvector {v}")

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