Problem $\backslash$#$1(25$ points$)$

In the following circuit:

$1)$ Find the mesh current equations for $\backslash (\backslash$mathrm$\{$I$\}1,\backslash$mathrm$\{$I$\}2\backslash )$ and I $3$ in terms of the reference designators $($i$.$e$.$ Vs$,$ Is$,$ R$1$ etc.$).(5$ points$)$

$2)$ Find the node voltages V$1$ and V$2$ in terms of mesh currents I$1,$ I$2$ and I$3$ and the reference designators. $(5$ points$)$

$3)$ Solve equations in $1)$ and $2)$ numerically using the values on the schematic. Create matrix. $(15$ points$)$ Note: There is a Super Mesh.