Problem 1.2 Consider the perceptron in two dimensions: h(x) = sign(wTx) where w = [uo, wl,W2)" and x [1,x1,x2)". Technically, x has three coordinates, but we call this perceptron two-dimensional because the first coordinate is fixed at 1 (a) Show that the regions on the plane where h(x) +1 and h(x)--1 are separated by a line. If we express this line by the equation x2 an +b, what are the slope a and intercept b in terms of wo, w, w2? (b) Draw a picture for the cases w = [1, 2, 3j" and w =-[1, 2, 3] In more than two dimensions, the +1 and -1 regions are separated by a hy perplane, the generalization of a line. Problem 1.2 Consider the perceptron in two dimensions: h(x) = sign(wTx) where w = [uo, wl,W2)" and x [1,x1,x2)". Technically, x has three coordinates, but we call this perceptron two-dimensional because the first coordinate is fixed at 1 (a) Show that the regions on the plane where h(x) +1 and h(x)--1 are separated by a line. If we express this line by the equation x2 an +b, what are the slope a and intercept b in terms of wo, w, w2? (b) Draw a picture for the cases w = [1, 2, 3j" and w =-[1, 2, 3] In more than two dimensions, the +1 and -1 regions are separated by a hy perplane, the generalization of a line