Suppose the softmax regression technique was applied to classify a data set that contains three classes C1,C2,C3. We minimize the objective function minimizef(w^)=P1p=1P[log(j=13ew^jTx^p)w^ypTx^p] over the training data set {(xp,yp),p=1,2,,P} where xpR21 and yp{1,2,3}, The minimizer is w^=[215140312]T (The sub-models are stacked in the order of w^1,w^2,w^3.) Assuming there are 3 samples in the test data set: x1(t)=[21]x2(t)=[12]x3(t)=[35] (Hint: e2.7 ) a) Apply the optimized model given above to classify each of the test samples. b) If x1(t)C3, what are the true probabilities for x1(t) belongs to each class, respectively? What are the predicted probabilities with the given optimal model w for x1(t) belongs to each class, respectively? c) Please show that w~=[324251401]T is also one optimal model with respect to the given objective function, i.e., f(w~)=f(w^). What is the predicted label for x3(t), when we apply w~ to do the classification