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3. Not all resistor networks can be easily simplified using the formulas for resistances in series and parallel. The following circuit, which has five resistors in a bridge configuration, is one such circuit R2 Nevertheless, it can still be analyzed as a three-loop circuit from which the current flowing through the voltage source can be calculated (a) Write down the 3x3 matrix equation which can be solved to determine the vector of currents in the three loops (b) Using Kramers rule, express the current flowing through the voltage source as the ratio of determinants of two 3 x 3 matrices (c) By expanding the expression found in part (b), find an expression for the equivalent single resistance, Requiv that would produce the same current flowing through the voltage source. To avoid a lot of tedious algebra, now would be a good time to learn how to use a symbolic manipulation program like Mathematica or Maple (d) Show that if Ri = R2-R12 and R3 R4-R3, then the equivalent resistance does not depend on the value of Ro. Explain why this should be expected

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