ONLY QUESTION $2$ PLEASE

Figure $1$: The circuit on the left is for Question $1.$ The circuit on the right is for Question $2.$

$2.$ Node$-$Voltage Analysis. Consider the right$-$hand circuit in Figure $1.$

$($a$)(4$ points$)$ Pick one ground node and formulate node$-$voltage equations for the circuit. Use the labels provided in the figure, indicate the final equations, circuit unknowns and how you handle the presence of voltage sources. What is the voltage $\backslash ($ v$\_\{3\}\backslash )$ across $\backslash ($ R$\_\{3\}\backslash )$ in terms of node voltages? Assume that all resistors values, $\backslash ($ R$\_\{$i$\},$ i$=1,2,3,4\backslash ),$ as well as $\backslash ($ v$\_\{$S$\_\{1\}\}\backslash )$ and $\backslash ($ v$\_\{$S$\_\{2\}\},$ i$\_\{$S$\}\backslash )$ are known values.

$($b$)(2$ bonus points$)$ Assuming that you have calculated the mesh currents in the circuit, what would be the power absorbed by $\backslash ($ R$\_\{4\}\backslash )?$

Do not modify the circuit diagram or the labels. You don't need to solve any equations!