Consider an electric circuit with n + 1 nodes, 1:0, . . . ,In. If there is a resistor connecting nodes 331 and 5:31, ' its resistance is denoted by :r'z-j > 0. The conductance between nodes 33%- and .733 is then a\"- = 1/sz- If :37; and my are not connected, rij = 00. Assume that there is a path connecting nodes 330 and mm and that we connect nodes .120 and arn to a battery to create a voltage difference of V across them. How can we nd the voltage difference across the other nodes, and the currents across the resistors? Let v0, . . . ,1)\" be the voltage of each node. The solution of this problem can be cast as an optimization problem to minimize the electrostatic energy of the system: 1 minimize chm, . . . ,9\") = i Z 013 - (vi by)? [1) 031(an 1. Explain how to compute oz vi for each pair of connected nodes. 2. Explain how to compute \"DZ for each node. 3. Ohm's law says that the current across each resistor is given by L25 2 (v1- vj) /r1j. Show that Kircho's law holds: N Zia-\"i=0, i=1,...,n71. (2) 1:0