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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:

def _get_initial_residual(self, x0):
        '''Return the projected initial residual.

        Returns :math:`MPM_l(b-Ax_0)`.
        '''
        if x0 is None:
            Mlr = self.linear_system.Mlb
        else:
            r = self.linear_system.b - self.linear_system.A*x0
            Mlr = self.linear_system.Ml*r

        PMlr, self.UMlr = self.projection.apply_complement(Mlr, return_Ya=True)
        MPMlr = self.linear_system.M*PMlr
        MPMlr_norm = utils.norm(PMlr, MPMlr, ip_B=self.linear_system.ip_B)
        return MPMlr, PMlr, MPMlr_norm