The voltage drop across a resistor is V = IR, The sum of all voltage drops in a

Question

The voltage drop across a resistor is V = IR, The sum of all voltage drops in a closed loop sum to zero (Kirchoff's Law). The previous two facts allow us to construct the following system of equations: R6I1 + R1(I1 - I2) + R2(I1 - I3) = V1, R3I2 + R4(I2 - I3) + R1(I2 - I1) = V2, R5I3 + R4(I3 - I2) + R2(I3 - I1) = V3. Let the resistances be given by R1 = 20, R2 = 5, R3 = 30, R4 = 25, R5 = 15, and let V2 = 0 and V3 = 50. We will be varying V1 throughout this exercise, and solving for the currents, I1, I2, and I3. Vary V1 from 50 to 100 in steps of 2 (i. e. , V1 = 50, 52, 54,. . . , 98, 100) and calculate I1, I2 and I3 as a function of the increasing V1 by solving the system above using LU-decomposition____ For the same V1 values from 50 to 100 in steps of 2, create a matrix B that is 3 by 26, one column for every new value of V1 (the second and third rows are the constant V2 and V3 values). Try solving the system AX = B in one fell swoop by using the backslash command: X=AB;.

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