Could you please help me to solve this problem? Thank you so much!

1. 7 marks (a) |4 marks Recall the definition of a convex set: We say a set C of points in R" is convex if for every pair x, y E C, all points on the line segment joining x and y are in C. Thus C is a convex set, by definition, if for every pair x, y E C and any 1 E [0, 1] we have Ax + (1 - ))y E C. Let A be an m x n matrix and b a given vector in Rm. Show that F = {x ER" : Ax