The problem is attached here, seems to be from matrix perturbation but what needs to be shown is unclear.

Problem 5: 23 points. We consider Ax = b, A is not singular. Assume that we perturb matrix A and vector b by a small amount: A + 5A, b + 5b The new solution x is itself perturbed as a result (A+5A)(x+5x) = b+5b Show that there exists a 6A and 5b such that ||5x||2 = IIA'lllz (II5AII2 Mac + 5x||2 + uo'buz) with 5x at 0