Please show all your work and reasoning!

Given the following 3-class classification problem:

C1: {(4, 1), (2, 3), (3, 5), (5, 4), (1, 6)}

C2: {(0, 2), (-2, 2), (-3, 2), (-2, 4)}

C3: {(1, -2), (3, -2)}

and the following single layer perceptron:

(a) Can the net learn to separate the samples, given that you want: if x Ci then yi = 1 and yj = -1 for j i. No need to solve for the weights, but justify your answer. (b) Add the sample (-1, 6) to C1. Repeat part (a).

x1 Input space x2