Forward Gaussian Elimination Using VRP and VRS:
Original [ a | b | p ] =
 [  2.178e+00  3.145e+00  9.138e+00 |  9.679e+01 | 0 ]
 [  1.456e+00  2.805e+00  6.731e+00 |  7.485e+01 | 1 ]
 [  1.688e+00  3.763e+00  2.341e+00 |  5.122e+01 | 2 ]
 0th Pivot: a[p[2]][0] =  1.688e+00;
k=0 Virtual Pivoted Form [ a | b | p | s ] =
 [  1.290e+00 -1.710e+00  6.117e+00 |  3.070e+01 | 2 |  9.138e+00 ]
 [  8.626e-01 -4.408e-01  4.712e+00 |  3.067e+01 | 1 |  6.731e+00 ]
 [  1.688e+00  3.763e+00  2.341e+00 |  5.122e+01 | 0 |  3.763e+00 ]
 1th Pivot: a[p[2]][1] = -1.710e+00;
k=1 Virtual Pivoted Form [ a | b | p | s ] =
 [  1.290e+00 -1.710e+00  6.117e+00 |  3.070e+01 | 2 |  6.117e+00 ]
 [  8.626e-01  2.577e-01  3.135e+00 |  2.276e+01 | 0 |  4.712e+00 ]
 [  1.688e+00  3.763e+00  2.341e+00 |  5.122e+01 | 1 |  3.763e+00 ]
Final Actual Pivoted Form [ Pa | Pb | p | s ] =
 [  1.688e+00  3.763e+00  2.341e+00 |  5.122e+01 | 0 |  3.763e+00 ]
 [  1.290e+00 -1.710e+00  6.117e+00 |  3.070e+01 | 1 |  6.117e+00 ]
 [  8.626e-01  2.577e-01  3.135e+00 |  2.276e+01 | 2 |  4.712e+00 ]
Back Substituted Results in Order of Solution:
 x[2] =  7.259e+00;
 x[1] =  8.012e+00;
 x[0] =  2.415e+00;
Answer: FGE with BackSubstition, VRP & VRS Results: x(approx) =
[  2.415e+00 ]
[  8.012e+00 ]
[  7.259e+00 ]
Equation substitution error of residual =  b-a*x(approx) = 
[  1.421e-14 ]
[  7.105e-15 ]
[  3.553e-15 ]
Residual Norm =  1.421e-14; b Norm =  9.679e+01;
Relative Residual = ||residual||/||b||=  1.468e-16