(Solved): 4. Consider the circuit below, (a) Use the loop-current method to obtain a set of three linearly i ...

4. Consider the circuit below, (a) Use the loop-current method to obtain a set of three linearly independent equations, in terms of the loop currents $I_1,I_2$ and $I_3$, and the sources $V_s$ and $I_s$, but no other variables, that can be used to determine the loop currents. Simplify your equations and write them with integer-valued coefficients. (b) Use the node-voltage method to obtain a set of three linearly independent equations, in terms of the node voltages $V_1,V_2$ and $V_3$, and the sources $V_s$ and $I_s$, but no other variables, that can be used to determine the node voltages. Simplify your equations and write them with integer-valued coefficients. (c) Is it known that $V_3=k_1{V}_s+k_2{I}_s$. Use superposition to determine the values of $k_1$ and $k_2$. (d) Assuming that $V_s=10\mathrm{V}$ and $I_s=1\mathrm{A}$, use your equations from part (a) to obtain the loop currents $I_1,I_2$ and $I_3$. It is fine to use calculators, software, or python to solve this problem but keep in mind that you might need to do it in an exam.