Big Circuit with Dependent Sources
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Following the node method, develop a set of simultaneous equations for the network shown below that can be solved to determine the unknown node voltages e_1, e_2 and e_3. Simplify your equations to the extent you can. Your equations should involve only those three variables (not i_1 or i_2) and any constants from the problem. You need not solve the set of equations for the node voltages.
Note that e_4 is not included in the analysis because it is directly sourced by the dependent voltage source from ground, and the source voltage can be expressed in terms of the first three node voltages. In this sense, it is treated like an independent voltage source. Nonetheless, describe how e_4 can be determined from e_1, e_2, and e_3 once the latter node voltages are determined.
For full credit, express each of your equations in the form \sum_i
a_ie_i = a_0, where e_i are the node potentials, a_i are constants that
scale each of the node potentials, and a_0 is a constant.
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