If you are given the following matrix, show that it is not a legitimate correlation matrix by creating an allocation to the three positions such that the variance is negative for that allocation (show the formula to verify that the variance is negative):
fake_corr = np.array([[1.0, -0.6, -0.5], [-0.6, 1.0, -0.7], [-0.5, -0.7, 1.0]])