Simplifying the equations yields:
(R1+R4) I1 + 0 - R4I3 = V.
R1 I1 - R2 I2 + R3I3 = 0 .
- R4 I1 + R5 I2 + (R3 + R4 + R5) I3 .
The simultaneous equations above can be seen as a matrix equation
M | I > = | V > ,
where M is the following resistance matrix
| R1+R4 | 0 | - R4 |
| R1 | - R2 | R3 |
| - R4 | R5 | R3 + R4 + R5 |
where | I > is the following current vector
| I1 |
| I2 |
| I3 |
and where | V > is the following voltage vector
| V |
| 0 |
| 0 |