4.2 ( ) www Consider the minimization of a sum-of-squares error function (4.15), and suppose that all of the target vectors in the training set satisfy a linear constraint aTtn + b = 0 (4.157)

where tn corresponds to the nth row of the matrix T in (4.15). Show that as a consequence of this constraint, the elements of the model prediction y(x) given by the least-squares solution (4.17) also satisfy this constraint, so that aTy(x) + b = 0. (4.158)

To do so, assume that one of the basis functions φ0(x) = 1 so that the corresponding parameter w0 plays the role of a bias.