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3. Consider the circuit depicted in the figure. R6 V₁ I₁ R₁ R₂ ^^^ MA V₂ 1₂ R4 ААА V3 MA АА R3 R, By using the two following facts: (i) the voltage drop across a resistor is V = IR and (ii) the sum of all voltage drops in a closed loop sum to zero, The currents 11, 12, and 13 are determined from the 3 x 3 system. R6I1 + R₁(I1 − I2) + R2(I1 − I3) = V₁ R312 + R4(I2 I3) + R₁(I2 − I1) = V/₂ R513 + R4(13 - 12) + R₂(I3 − I1) = V3
where R₁ = 15, R₂ = 20, R3 = 10, R4 = 25, R5 = 40, R6 = 30, V₂ = 50, V3 = 150, and V₁ will be variable. In this form, the associated matrix is strictly diagonal dominant. (a) Vary V₁ from 0 to 100 in steps of 2 (i.e. V₁ = 0, 2, 4, ..., 100) and calculate I₁, 12, and I3 as a function of increasing V₁ by solving the system with the standard backslash (matlab) or solve (python) command. Save your results in a matrix of 3 columns and 51 rows where the first, second and third column are I₁, I2 and 13 respectively. Save this resulting matrix as A9. (b) Repeat part (a), but use LU decomposition to solve the system for each V₁. Again, save the resulting matrix of 3 columns and 51 rows as A10.