5. (a) Let A = {(x,y) = 2 x+2y 37} {(x,y) = 2 |ex>y} Prove that A is compact. n Show that any convex subset C of " is connected. (b) 6. Show that the set {log p p prime number} is linearly independent over . 7. 8. Let V be the vector space of all polynomial functions of degree 2, and let D VV denote the derivative map P a P' on V. Show that D is nilpotent and that D is not diagonalizable. Let A and B be two 3 x3 complex matrices. Show that A and B are similar if and only if XA = XB and = B, where XA. XB are characteristic polynomials of A, B, respectively and , B are minimal polynomials of A, B, respectively.