Use Matlab to solve the question

Computing the Fourier transform of a vector x is an important problem. To investigate the conditioning of this problem, use Matlabs fft function. Let x = randn(2^20,1) and let y = (1+eps)*x. Compare the relative error in fft(y) to the relative error in y. Repeat this experiment four more times. Is the problem well-conditioned?

Note: The relative error between two scalars a and b, where b is the true or reference value, is abs((a-b)/b). If a and b are vectors, use norm(a-b)/norm(b).