Suppose P n m is the blow up of P n at a linear subspace of dimension m, L = {L 1 , . . . , Lr} is a (not necessarily full) strong exceptional collection of line bundles on P n m . Let Q be the quiver associated to this collection. One might wonder when is P n m the moduli space of representations of Q with dimension vector (1, . . . , 1) for a suitably chosen stability condition θ: S ∼ = M θ . In this paper, we achieve such isomorphism using L of length 3. As a result, P n m is the moduli space of representations of a very simple quiver. Moreover, we realize the blow up as morphism of moduli spaces for the same quiver.