#### Solving currents in a Circuit (7 × 7 system)

We solve this using a computer as follows. We just write the coefficient matrix on the left, find the inverse (raise the matrix to the power -1) and multiply the result by the constant matrix.

You can use Matlab, Mathcad or similar math software to do this. Wolfram|Alpha is a free alternative.

`X=[(72,0,-17,-35,0,0,0),
(0,122,-35,0,0,0,-87),
(0,-87,-34,0,0,-72,233),
(-17,-35,149,0,-28,-35,-34),
(0,0,-28,-43,105,-34,0),
(0,0,-35,0,-34,141,-72),
(-35,0,0,105,-43,0,0)]^-1
[(-26),(34),(-4),(-13),(-27),(24),(5)]`

`=[(-0.46801),(0.42932),(5.193xx10^-3),(-0.22243),(-0.27848),(0.21115),(0.20914)]`

The answer means that the currents in this circuit are (to 4 decimal places):

`I_1 = -0.4680\ "A"`

`I_2= 0.4293\ "A"`

`I_3= 0.0005\ "A"`

`I_4= -0.2224\ "A"`

`I_5= -0.2785\ "A"`

`I_6= 0.2112 \ "A"`

`I_7= 0.2091 \ "A"`