A Vector space V over a field F is a set of elements which i

A Vector space V over a field F is a set of elements which is closed under two operations and. The operations satisfy that for any u, v, w V and c, d F u v = v u, u (v w) = (u v) w, theta V such that u theta = u, given u V, (- u) V such that u (-u) = theta, c (u v) = c u c v c (d u) = (cd) u, (c+d) u = c u d u, and 1 u = u.

Solution

there is nothing to prove. As definition as well as required properties both are already given for above defined vector space.