1. The problem statement, all variables and given/known data Given the following circuit: Calculate the currents I1, I2, and I3 The given resistances are: r: 1.05 ohm R1: 11.7 Ohm R2: 10.5 Ohm R3: 7.20 Ohm R4: 14.3 Ohm R5: 18.8 Ohm The given emf's are: E1 = E2: 9.0 V E3: 3.0 V 2. Relevant equations We know Kirchhoff's laws for current and voltage. Namely, Iin = Iout for any junction, and voltage around any loop must = 0. 3. The attempt at a solution I attempted to use Kirchhoff's voltage laws around the big loop (all the way around the outside), the upper (top) loop, and the lower (bottom) loop. Then, I put these into a matrix, and tried to use the reduced row echelon form (rref) to solve for the currents. Big loop: E3 - I3r - I3R5 - I1R1 + E1 - I1r - I1R3 - I3R4 = 0 This is equivalent to: I1(-R1 - r - R3) + I2(0) + I3(-r - R5 - R4) = -E3 - E1 Top loop: E2 - I2r - I2R2 - I1R1 + E1 - I1r - I1R3 = 0 Equivalent to: I1(-R1 - r - R3) + I2(-r - R2) + I3(0) = E2 - E1 Bottom loop: E3 - I3r - I3R5 + I2R2 + I2r - E2 - I3R4 = 0 Equivalent to: I1(0) + I2(R2 + r) + I3(-r - R5 - R4) = -E3 + E2 Resultant matrix Code: [(-R1 - r - R3) 0 (-r - R5 - R4) ] [ I1 ] [ -E3 - E1 ] [(-R1 - r - R3) (-R2 - r) 0 ] [ I2 ] = [ E2 - E1 ] [ 0 (R2 + r) (-r - R5 - R4) ] [ I3 ] [ -E3 + E2 ] However, the rref of this matrix ends up with a row of all 0's (implying infinite solutions). Therefore, I'm assuming there is a mistake in how I went around the loops and setup the equations. Can anyone help?