Throughout, let k be a field. Question 1 Let Q be a quiver and set A=kQ. For i E Qo, set (Ae:)1 = Ae; n A21, the submodule of Ae, generated by all paths of length at least one. a) Show that for i # j Qo, the modules S := Ae:/(Ae:) and S; := Ae;/(Ae;) are non-isomorphic simple modules b) Realise S, as a representation of the quiver Q. [No proof required.) Throughout, let k be a field. Question 1 Let Q be a quiver and set A=kQ. For i E Qo, set (Ae:)1 = Ae; n A21, the submodule of Ae, generated by all paths of length at least one. a) Show that for i # j Qo, the modules S := Ae:/(Ae:) and S; := Ae;/(Ae;) are non-isomorphic simple modules b) Realise S, as a representation of the quiver Q. [No proof required.)