$1.$ The op$-$amp shown is ideal. $(15$ points$)$

a$.$ What assumptions are necessary to assume op$-$amp is ideal?

b$.$ What op$-$amp configuration is this?

c$.$ Find $\backslash ($ v$\_\{0\}\backslash )$ in terms of $\backslash ($ v$\_\{$s$\}\backslash ).$

d$.$ Find the range of $\backslash (\backslash$mathrm$\{$v$\}\_\{\backslash$mathrm$\{$s$\}\}\backslash )$ that will allow the op$-$amp to operate in its linear region.

e$.$ What happens to $\backslash (\backslash$mathrm$\{$v$\}\_\{0\}\backslash )$ outside this region?