Read the result
The unknown vector represents currents. The residual tells you whether the computed currents satisfy the original circuit equations.
Circuit systems
Kirchhoff Linear System Example
Solve loop-current style equations as a matrix system A i = v.
Formula
A i = v
Result
Worked substitution
Once circuit laws have produced the equations, the remaining work is linear algebra.
Where it helps
Use it after writing Kirchhoff loop equations, before interpreting the current directions physically.
Common slip
This is not a circuit-diagram parser. The quality of the result depends on the equations you enter.
Try it
Increase voltage 1 and check whether the first current responds in the direction you expect.