4. For each sentence, if it is true, please explain; if it is false, please provide...

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4. For each sentence, if it is true, please explain; if it is false, please provide a counterexample. 1) If there is a vector y # 0 such that Ay = 0, then the polyhedron P={x = R^: Ax b} 0 does not have an extreme point. 2) Every nonzero polyhedral cone is the convex hull of its extreme rays. 4) Let A Rmxn be a fixed matrix. The set of all b Rm for which the constraints Ax b are feasible (i.e., {b = Rm: 3x, Ax > b} is convex. 4. For each sentence, if it is true, please explain; if it is false, please provide a counterexample. 1) If there is a vector y # 0 such that Ay = 0, then the polyhedron P={x = R^: Ax b} 0 does not have an extreme point. 2) Every nonzero polyhedral cone is the convex hull of its extreme rays. 4) Let A Rmxn be a fixed matrix. The set of all b Rm for which the constraints Ax b are feasible (i.e., {b = Rm: 3x, Ax > b} is convex.