Figure $8\mathrm{.}9$

Using mesh analysis & determinants, find the following for the circuit in Figure $8\mathrm{.}9.$ Show all calculations. Show direction of each current. $(5$ points each$)$

a$)l_{R1}q,$

b$)l_{R2}q,$

c$)I_{R}q,$

d$)I_{R4}q,$

e$)I_{RS}q,$

Using nodal analysis, find the voltage at nodes $N_1(V_1)$ and $N_2(V_2)$ for the circuit in Figure $8\mathrm{.}9.$ Show all calculations. $(5$ points each$)$