$20$ pts$)$ Consider the perceptron in two dimensions h$($x$)=$ sign$($w$$x$)$ where

w $=[$w$0,$ w$1,$ w$2]$ and x $=[1,$ x$1,$ x$2].$ Note, x has three coordinates, but we call this a $2$D perception because the first coordinate is fixed to $1.$

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 x$2=$ ax$1+$ b$,$ what are the slope of a and the intercept b in terms of w$0,$ w$1,$ w$2?$

B$.$ Draw pictures for the cases w $=[1,1,1]$ and w $=[1,2,3].$