Problem $6\mathrm{.}1($Inverse Function Theorem$).$ Let $$G$($u$,$ v$)=($uev $,$ u$2+$ v$),$ and consider the point $($u$,$ v$)=(1,0),$ for which $$G$(1,0)=(1,1).1.[2$ pts$]$ Use the Inverse Function Theorem to show that $$G is locally invertible near $(1,0).2.[1$ pt$]$ Compute the Jacobian matrix of the inverse map $$G$-1$ at the point $(1,1).$Problem $6\mathrm{.}1($Inverse Function Theorem$).$ Let vec$($G$)($u$,$v$)=($ue$^($v$),$u$^(2)+$v$),$ and consider the point $($u$,$v$)=(1,0),$ for which vec$($G$)(1,0)=(1,1).[2$ pts$]$ Use the Inverse Function Theorem to show that vec$($G$)$