Hi, I'm trying to use Kirchoff's voltage law to find a system of equations which I can use to find I1, I2, I3, I4, and I5; which are the respective currents going through each resistor in the image. I have 5 unknowns so I need to find 5 non redundant equations. The problem is, every system of equations I come up with is singular. In other words... I am trying to set up a matrix equation ##A x = b## but my matrix A keeps having determinant zero! Is there any general rule to follow in order to find a non redundant set of equations? This is really time consuming! If you are curious, here is an example system which I came up with, but in some way it's redundant. Code (Text): V = R1 I1 + R4 I4 V = R2 I2 + R5 I5 V = R1 I1 + R3 I3 + R5 I5 V = R2 I2 - R3 I3 + R4 I4 0 = R1 I1 - R2 I2 + R4 I4 - R5 I5 V is the voltage of the battery.