Please answer every sub$-$question. Thanks! $15\mathrm{.}1.$ Each of the following problems describes an algorithm implemented on a computer satisfying the axioms $(13\mathrm{.}5)$ and $(13\mathrm{.}7).$ For each one, state whether the algorithm is backward stable, stable but not backward stable, or unstabie, and prove it or at least give a reasonably convincing argument. Be sure to follow the definitions as given in the text $($a$)$ Data:$$EC$.$ Solution: $2$z$,$ computed as $($b$)$ Data: C$.$ Solution ; $2,$ cuillpuLed as $($c$)$ Data: x C$->).$ Solution: $1,$ computed as rr$.($A machine satisfying $(13\mathrm{.}6)$ will give exactly the right answer, but our definitions are based on the weaker condition $(13\mathrm{.}7).)($d$)$ Data: C$.$ Solution: $0,$ computed as $\backslash$Theta $".($Again$,$ a real machine may do better than our definitions based on $(13\mathrm{.}7).)($e$)$ Data: none. Solution: e$,$ computed by summing $,1/$k$!$ from left to right using and $,$ stopping when a summand is reached of magnitude $($f$)$ Data: none. Solution: e$,$ computed by the same algorithm as above except with the series summed from right to left