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## 07 Jul n Linear least squares problem Ax≅b, we seek a solution x su

n Linear least squares problem Ax≅b, we seek a solution x such that the residual‖b−Ax‖22is minimized. A regularization term can be included to give preference to a solution x with a desired property. This regularization is minimizing,‖b−Ax‖22+α‖x‖22.This is equivalent to the augmented least squares problem [Aα‾‾√I]x≅[b0]You are given a matrix A, vector b and scalar α. Calculate x such that it minimizes the residual for Ax≅b and x2 such that it minimizes the regularization condition. Also calculate the residual and norm for both.code belowimport numpy as npimport scipy.sparseINPUT: A: numpy array of shape (m, n) b: numpy array of shape (m,) alpha: Python floatOUTPUT: x: numpy array of shape (n,) that minimizes the residual. x2: numpy array of shape (n,) that minimizes the L2-regularization condition. norm_x: Norm of x. norm_x2: Norm of x2. residual_x: Norm of the residual of x. residual_x2: Norm of the residual of x2.n = np.random.randint(100, 200)A = scipy.sparse.diags([-1,2,-1],[-1,0,1],shape=(n, n//4)).Ab = np.ones(n)alpha = 1.5

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