1. The problem statement, all variables and given/known data Let V be a vector space over R. let Φ1, Φ2 ∈ V* (the duel space) and suppose σ:V→R, defined by σ(v)=Φ1(v)Φ2(v), also belongs to V*. Show that either Φ1 = 0 or Φ2 = 0. 2. Relevant equations N/A 3. The attempt at a solution Since σ is also an element of the duel space, it is linear, so σ(v+u)=σ(v)+σ(u). Translating both sides into terms of Φ1 and Φ[SUB}2[/SUB], I came up with the equation (1) Φ1(v)Φ2(u)+Φ1(u)Φ2(v)=0. Doing the same with σ(av+bu) and plugging in equation (1) produced the equation (2) a2Φ1(v)Φ2(v)+b2Φ1(u)Φ2(u)=aΦ1(v)Φ2(v)+bΦ1(u)Φ2 This is where I got stuck, perhaps there is a trick I am not seeing to this equation or perhaps I approached this the wrong way. Any help would be appreciated.