*****MATLAB*****

A circuit of resistors: Consider the following circuit of resistors: All the resistors have the same resistance R. The power rail at the top is at voltage V_+ = 5V. The question is, what are the other four voltages, V_1 to V_4? To answer this question we use Ohm's law and the Kirchhoff current law, which says that the sum of all currents that flow out of and/or into any junction in a circuit must be zero (flow in with +ve sign and flow out with -ve sign). Thus for the junction at voltage V_1, for instance, we have V_+ - V_1/R - V_1 - V_2/r - V_1 - V_3/R - V_1 - V_4/R = 0 or equivalently 4V_1 - V_2 - V_3 - V_4 = V_+ (a) Derive similar equations for the other three junctions (V_2, V_3 and V_4) with unknown voltages, and then create the Ax = b system where x = (V_1 V_2 V_3 V_4) Determine matrices A and b. (b) Write a Matlab program to solve the four resulting linear equations using the determinant method and hence find the four voltages. (c) Compare your results with the Matlab's backslash operator, ie. x = A\b