Kirchhoff's Rules Homework Solution

[ma18]

Homework Statement

Find Kirchoff's laws for this
http://postimg.org/image/d78dvdg5f/

(Actual problem has a bit more but I can do that part.)

Homework Equations

Loop rule
Junction rule

The Attempt at a Solution

I got the following equations

2e - 4i_4 - 2i_2 = 0
e - 3i_3 - i_1 = 0
e - 4i_4 - i_1 = 0
2e - 3i_3 - 2i_2 = 0
3e - i_1 - 2i_2 = 0

I used these in a matrix but when I reduced to rref I got zero's for the currents which doesn't make sense.

Thanks,

P.S This is from a 2nd year Uni course

 

[Simon Bridge]

It helps to label your diagram.
You appear to have put $e=\varepsilon/R$
I don't see where 3e comes from.

You have three loops - but 5 loop equations - this means that you will get zero lines in the matrix (some of rows are linear combinations of the others) and you appear to have no junction-rule equations: these will not have any e's in them. So your system of equations may be incomplete.