Question 1202978
<pre>
{{{system(z[1]i[1] + z[3]i[3] = V,
z[2]i[2] - z[3]i[3] = 0,
i[1] - i[2] - i[3]= 0)}}}

Line up the i's with like subscripts vertically:

{{{system(matrix(3,7,
z[1]i[1],   "",      "",""+"",z[3]i[3],""="",V, 
      "",   "",z[2]i[2],""-"",z[3]i[3],""="",0,
    i[1],""-"",    i[2],""-"",    i[3],""="",0))}}}

Make the denominator determinant D, whose elements are all
the coefficients of the i's on the left of the equal signs:

{{{matrix(1,3,

D, ""="", abs(matrix(3,3,

z[1],   0, z[3],
   0,z[2], -z[3],
   1,  -1,    -1)))}}}{{{""=""}}}{{{z[1]abs(matrix(2,2,z[2],-z[3],-1,-1))}}}{{{""-""}}}{{{0*abs(matrix(2,2,0,-z[3],1,-1))}}}{{{""+""}}}{{{z[3]abs(matrix(2,2,0,z[2],1,-1))}}}{{{""=""}}}{{{z[1]*((z[2])(-1^"")^""-(-z[3])(-1^"")^"")}}}{{{""-""}}}{{{0}}}{{{""+""}}}{{{z[3]*((0^"")(-1^"")-(z[2])(1^"")^"")}}}{{{""=""}}}

{{{z[1](-z[2]-z[3])+z[3](0-z[2])}}}{{{""=""}}}{{{-z[1]z[2]-z[1]z[3]-z[3]z[2])}}}

Now we make the numerator determinants.
The numerator determinant for the 1st variable D<sub>i1</sub> is formed by
replacing the 1st column of the denominator determinant D by the numbers on the
right of the equal signs:

{{{matrix(1,3,

D[i1], ""="", abs(matrix(3,3,

   V,   0, z[3],
   0,z[2], -z[3],
   0,  -1,    -1)))}}}{{{""=""}}}{{{V*abs(matrix(2,2,z[2],-z[3],-1,-1))}}}{{{""-""}}}{{{0*abs(matrix(2,2,0,-z[3],0,-1))}}}{{{""+""}}}{{{z[3]abs(matrix(2,2,0,z[2],0,-1))}}}{{{""=""}}}{{{V*((z[2])(-1^"")^""-(-z[3])(-1^"")^"")}}}{{{""-""}}}{{{0}}}{{{""+""}}}{{{z[3]*((0^"")(-1^"")-(z[2])(0^"")^"")}}}{{{""=""}}}

{{{V(-z[2]-z[3])+z[3](0-0)}}}{{{""=""}}}{{{-V*(z[2]+z[3])}}}

The numerator determinant for the 2nd variable D<sub>i2</sub> is formed by
replacing the 2nd column of the denominator determinant D by the numbers on the
right of the equal signs:

{{{matrix(1,3,

D[i2], ""="", abs(matrix(3,3,

   z[1],   V, z[3],
   0,   0, -z[3],
   1,  0,    -1)))}}}{{{""=""}}}{{{z[1]*abs(matrix(2,2,0,-z[3],0,-1))}}}{{{""-""}}}{{{V*abs(matrix(2,2,0,-z[3],1,-1))}}}{{{""+""}}}{{{z[3]abs(matrix(2,2,0,0,1,0))}}}{{{""=""}}}{{{z[1]*((0)(-1^"")^""-(-z[3])(0^"")^"")}}}{{{""-""}}}{{{0}}}{{{""+""}}}{{{z[3]*((0^"")(0^"")-(0)(1^"")^"")}}}{{{""=""}}}

{{{z[1](0^""-0)-V((0^"")(-1^"")-(-z[3])(1^"")^"")}}}{{{""=""}}}{{{-V*(z[3])}}}

The numerator determinant for the 3rd variable D<sub>i3</sub> is formed by
replacing the 3rdd column of the denominator determinant D by the numbers on the
right of the equal signs:

{{{matrix(1,3,

D[i3], ""="", abs(matrix(3,3,

z[1],   0, V,
   0,z[2], 0,
   1,  -1,  0)))}}}{{{""=""}}}{{{z[1]abs(matrix(2,2,z[2],-0,-1,0))}}}{{{""-""}}}{{{0*abs(matrix(2,2,0,0,1,0))}}}{{{""+""}}}{{{V*abs(matrix(2,2,0,z[2],1,-1))}}}{{{""=""}}}{{{z[1]*((z[2])(0^"")^""-(0)(-1^"")^"")}}}{{{""-""}}}{{{0}}}{{{""+""}}}{{{V*((0^"")(-1^"")-(z[2])(1^"")^"")}}}{{{""=""}}}

{{{z[1](0^""-0)+V(0-z[2])}}}{{{""=""}}}{{{-Vz[2])}}}

Finally, we put the numerators over the same denominator D:

{{{i[1]}}}{{{""=""}}}{{{D[i1]/D^""}}}{{{""=""}}}{{{(-V*(z[2]+z[3]))/(-z[1]z[2]-z[1]z[3]-z[3]z[2])}}}{{{""=""}}}{{{(V*(z[2]+z[3]))/(z[1]z[2]+z[1]z[3]+z[3]z[2])}}}

{{{i[2]}}}{{{""=""}}}{{{D[i2]/D^""}}}{{{""=""}}}{{{(-V*z[3])/(-z[1]z[2]-z[1]z[3]-z[3]z[2])}}}{{{""=""}}}{{{(V*z[3])/(z[1]z[2]+z[1]z[3]+z[3]z[2])}}}

{{{i[3]}}}{{{""=""}}}{{{D[i3]/D^""}}}{{{""=""}}}{{{(-V*z[2])/(-z[1]z[2]-z[1]z[3]-z[3]z[2])}}}{{{""=""}}}{{{(V*z[2])/(z[1]z[2]+z[1]z[3]+z[3]z[2])}}}

Edwin</pre>