Simply put, you can't.

The Gauss-Seidel method is an iterative method to solve a system of equations but it does not use (or return) the matrix inverse. If all you are interested in is the matrix inverse, you will have to find a different algorithm (such as LU decomposition or a modified version of Gauss-Jordan). If all you are interested in is solving a system of linear equations, the Gauss-Seidel method will do just fine.

Thank's for you explaination ! I wanna implement the Gauss-Seidel Linear solve system. Forget the matrix inversion, I need knows only how a get this in VB 5.0. Can you help me ?

Here is an implementation of Gauss-Seidel in Visual Basic. Before you use it though, there are a few words of warning: the Gauss-Seidel method works best on diagonally dominant systems of equations (ie the elements on the diagonal are  larger than the other elements in the array). I have included a function to test for this condition (the GaussSeidelConverge function) if this function returns "true", the system is guaranteed to converge; if it does not return "true" it is not guaranteed (but that does not necessarily mean it will diverge). One of the optional arguments to the main routine is "RelaxCoeff", this is a relaxation coefficient that may help with the solving process. This coefficient can take on values from 0 to 2 (1 is the default, it is the same as not using relaxation). If the system is guaranteed to converge, you can use a value between 1 and 2 to make in converge faster; if the system is not guaranteed to converge setting it to a value between 0 and 1 may help keep things on track.

My implementation is by no means "bulletproof" but it should get you headed in the right direction. Hope it helps you.

PS if you have any questions about it please ask, and if you make any improvements to it I'd like to see them!
OK here's the code:

'10/15/2001
'Module to perform Gauss-Seidel algorithm
'to solve a system of linear equations

'as is, these functions expect 0 based arrays

Option Explicit

Public Function NormalizeSystem(Coefficients() As Double, Constants() As Double)
As Boolean

  Dim dblDummy As Double
  Dim i As Integer
  Dim j As Integer

  On Error GoTo ErrorNormalizeSystem

  For i = 0 To UBound(Coefficients(), 1)
    dblDummy = Coefficients(i, i)
    For j = 0 To UBound(Coefficients(), 2)
      Coefficients(i, j) = Coefficients(i, j) / dblDummy
    Next j
    Constants(i) = Constants(i) / dblDummy
  Next i

  NormalizeSystem = True
  Exit Function

ErrorNormalizeSystem:
  NormalizeSystem = False

End Function

Public Function GaussSeidel(Coefficients() As Double, _
      Constants() As Double, _
      Unknowns() As Double, _
      Optional ErrorAllow As Single = 0.001, _
      Optional MaxIterations As Integer = 100, _
      Optional RelaxCoeff As Single = 1) As Boolean

  Dim intIterations As Integer
  Dim blnSentinel As Boolean
  Dim dblError As Double
  Dim dblOld As Double
  Dim dblSum As Double
  Dim i As Integer, j As Integer

  NormalizeSystem(Coefficients(), Constants())

  If ErrorAllow <= 0 Then ErrorAllow = 0.0001
  If RelaxCoeff < 0 Then RelaxCoeff = 0
  If RelaxCoeff > 2 Then RelaxCoeff = 2

  intIterations = 0
  blnSentinel = False

  On Error GoTo ErrorGaussSeidel

  Do While (intIterations < MaxIterations) And (blnSentinel = False)
    'blnSentinel = True
    intIterations = intIterations + 1

    'loop through the equations
    For i = 0 To UBound(Coefficients(), 1)
      dblOld = Unknowns(i)
      dblSum = Constants(i)

      'loop through the coefficients in the equation
      For j = 0 To UBound(Coefficients(), 2)

        If i <> j Then
          dblSum = dblSum - Coefficients(i, j) * Unknowns(j)
        End If

      Next j

      Unknowns(i) = RelaxCoeff * dblSum + (1 - RelaxCoeff) * dblOld

      If (blnSentinel = False) And (Unknowns(i) <> 0) Then
        dblError = Abs((Unknowns(i) - dblOld) / Unknowns(i)) * 100
      End If

    Next i

    If dblError <= ErrorAllow Then
      blnSentinel = True
      GaussSeidel = True
    End If
  Loop

  Exit Function

ErrorGaussSeidel:
  GaussSeidel = False

End Function

Public Function GaussSeidelConverge(Coefficients() As Double) As Boolean

  Dim i As Integer, j As Integer
  Dim sum As Double

  For i = 0 To UBound(Coefficients(), 1)
    sum = 0
    For j = 0 To UBound(Coefficients(), 2)
      If i <> j Then
        sum = sum + Abs(Coefficients(i, j))
      End If
    Next j
    If sum > Abs(Coefficients(i, i)) Then
      GaussSeidelConverge = False
      Exit Function
    Else
      GaussSeidelConverge = True
    End If
  Next i

End Function