[20 pts] Perceptron. Using the following observations from two classes (U U1 and U2) : U1:{(0,0)T,(1,1)T} and U2:{(1,0)T,(0,1)T}. Assume that the correction coefficient is C=1, and the initial weight vector is w(1)= (0,0,0)T. (NOTE: this weight is represented in canonical form with three dimensions.) a) [10 pts] Calculate the decision function weights iteratively until they converge. To get full credits, show updated weights on each iteration to demonstrate how they converge. Upon convergence, write the decision function analytical form. NOTE: Do NOT forget to convert the four 2-D points in the 2-D plane to 3-D canonical vector representation before applying weight adjustment rules learned in class lecture. b) [10 pts] Plot the 4 points and the decision boundary. NOTE: Please label axes, point symbols (eg. class U1 with ' x 's and U2 with ' o 's), and show the decision boundary equation clearly on the figure to receive full credit