Maxima 5.36.1 http://maxima.sourceforge.net
using Lisp SBCL 1.2.11-1.fc22
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) eqns:[-i1 + ix + iE = 0,
       i1 - i0 - i2 = 0,
      -iE + i2 - i3 = 0,
       i0 - ix + i3 = 0,
      -i1*R1  - i2*R2         = -E,
       i1*R1  + i0*R0 + ix*Rx =  0, 
       i2*R2  + i3*R3 - i0*R0 =  0
];
(%o1) [iE + ix - i1 = 0, (- i2) + i1 - i0 = 0, (- iE) - i3 + i2 = 0, 
(- ix) + i3 + i0 = 0, (- i2 R2) - i1 R1 = - E, i1 R1 + i0 R0 + ix Rx = 0, 
i3 R3 + i2 R2 - i0 R0 = 0]
(%i2) vars : [i0,i1,ix,i2,i3,iE];
(%o2)                      [i0, i1, ix, i2, i3, iE]
(%i3) soln : linsolve(eqns,vars),factor;

solve: dependent equations eliminated: (4)
(%o3) [i0 = - (E (R1 R3 - Rx R2))/(R1 R2 R3 + R0 R2 R3 + Rx R2 R3 + R0 R1 R3
 + Rx R1 R3 + Rx R1 R2 + Rx R0 R2 + Rx R0 R1), 
i1 = (E (R0 R3 + Rx R3 + Rx R2 + Rx R0))
/(R1 R2 R3 + R0 R2 R3 + Rx R2 R3 + R0 R1 R3 + Rx R1 R3 + Rx R1 R2 + Rx R0 R2
 + Rx R0 R1), ix = - (E (R1 R3 + R1 R2 + R0 R2 + R0 R1))
/(R1 R2 R3 + R0 R2 R3 + Rx R2 R3 + R0 R1 R3 + Rx R1 R3 + Rx R1 R2 + Rx R0 R2
 + Rx R0 R1), i2 = (E (R1 R3 + R0 R3 + Rx R3 + Rx R0))
/(R1 R2 R3 + R0 R2 R3 + Rx R2 R3 + R0 R1 R3 + Rx R1 R3 + Rx R1 R2 + Rx R0 R2
 + Rx R0 R1), i3 = - (E (R1 R2 + R0 R2 + Rx R2 + R0 R1))
/(R1 R2 R3 + R0 R2 R3 + Rx R2 R3 + R0 R1 R3 + Rx R1 R3 + Rx R1 R2 + Rx R0 R2
 + Rx R0 R1), iE = (E (R1 R3 + R0 R3 + Rx R3 + R1 R2 + R0 R2 + Rx R2 + R0 R1
 + Rx R0))/(R1 R2 R3 + R0 R2 R3 + Rx R2 R3 + R0 R1 R3 + Rx R1 R3 + Rx R1 R2
 + Rx R0 R2 + Rx R0 R1)]
(%i4) I:i0,soln,factor;
(%o4) - (E (R1 R3 - Rx R2))/(R1 R2 R3 + R0 R2 R3 + Rx R2 R3 + R0 R1 R3
                                   + Rx R1 R3 + Rx R1 R2 + Rx R0 R2 + Rx R0 R1)
(%i5) A:augcoefmatrix(eqns,vars);
                    [  0    - 1    1    0     0    1   0 ]
                    [                                    ]
                    [ - 1    1     0   - 1    0    0   0 ]
                    [                                    ]
                    [  0     0     0    1    - 1  - 1  0 ]
                    [                                    ]
(%o5)               [  1     0    - 1   0     1    0   0 ]
                    [                                    ]
                    [  0    - R1   0   - R2   0    0   E ]
                    [                                    ]
                    [  R0    R1   Rx    0     0    0   0 ]
                    [                                    ]
                    [ - R0   0     0    R2   R3    0   0 ]
(%i6) U:echelon(A),factor;
(%o6) matrix([1, - 1, 0, 1, 0, 0, 0], [0, 1, - 1, 0, 0, - 1, 0], 
          R2          E
[0, 0, 1, --, 0, 1, - --], [0, 0, 0, 1, - 1, - 1, 0], 
          R1          R1
                    R1 R2 + R0 R2 + R0 R1
[0, 0, 0, 0, 1, -----------------------------, 
                R1 R3 + R1 R2 + R0 R2 + R0 R1
              E R0
- -----------------------------], [0, 0, 0, 0, 0, 1, 
  R1 R3 + R1 R2 + R0 R2 + R0 R1
- (E (R1 R3 + R0 R3 + Rx R3 + R1 R2 + R0 R2 + Rx R2 + R0 R1 + Rx R0))
/(R1 R2 R3 + R0 R2 R3 + Rx R2 R3 + R0 R1 R3 + Rx R1 R3 + Rx R1 R2 + Rx R0 R2
 + Rx R0 R1)], [0, 0, 0, 0, 0, 0, 0])
(%i7) matrix_size(A);
(%o7)                               [7, 7]
(%i8)