Each of the following problems describes an algorithm implemented on a computer satisfying the axioms (13.5) and (13.7). for each one, state whether the algorithm is backwad stable, stable but not backward stable, or unstable, and prove it or at least give a reasonably convincing argument. be sure to follow the definitions as given in the text. (a) data: x e c. solution: 22, computed as x q x. (b) data: x e c. solution: x2, computed as x @ x. (c) data: x e c \{o). solution: 1,computed as x @x. (a machine satisfying (13.6) will give exactly the right answer, but our definitions are based on the weaker condition (13. (d) data: x e c. solution: 0,computed as x x. (again, a real machine may do better than our definitions based on (13.