In linear algebra,

**Gaussian elimination **is an algorithm for solving systems of linear equations, finding the rank of a matrix, and calculating the inverse of an invertible square matrix
The following is a sample of VBA excel code created by the author:
Private Sub Clear_Click()
Application.ScreenUpdating = False
Dim ans As String
ans = MsgBox("Data will be cleared. Please confirm ", vbYesNo + vbExclamation)
If ans = vbNo Then End
Sheets(8).Activate
'clear content of matrix
Sheets(8).Range("A10:IV1000").Select
Selection.ClearContents
Sheets(8).Cells(3, 2).Select
End Sub
Private Sub Compute_Click()
Dim N, div, multi As Integer
'reading data
N = Sheets(8).Cells(3, 2).Value
ReDim c(N, N + 1)
For i = 1 To N
For j = 1 To N + 1
c(i, j) = Sheets(8).Cells(i + 10, j + 3).Value
Next j
Next i
'ensure c(1, 1) <> 0
If c(1, 1) = 0 Then Call msg0 Else
'forward elimination of pivot row
For i = 1 To N
div = c(i, i)
For j = i To N + 1
c(i, j) = c(i, j) / div
Next j
For k = i + 1 To N
multi = c(k, i)
For j = i To N + 1
c(k, j) = c(k, j) - multi * c(i, j)
Next j
Next k
Next i
'back substitution
For i = N To 0 Step -1
For k = N To i + 1 Step -1
c(i, N + 1) = c(i, N + 1) - c(i, k) * c(k, N + 1)
Next k
Next i
'value of unknown
For i = 1 To N
Sheets(8).Cells(i + 10, 1) = c(i, N + 1)
Next i
End Sub
Sub msg250()
MsgBox ("n value is limit to 250 only!")
End
End Sub
Sub msg0()
MsgBox ("C(1,1) is equal to 0")
End
End Sub
Private Sub GenerateGE_Click()
Dim N As Integer
Dim ans As String
Application.ScreenUpdating = False
Sheets(8).Activate
'N as number of row or column
N = Sheets(8).Cells(3, 2).Value
'limit N to 250
If N > 250 Then Call msg250 Else
For i = 1 To N
Sheets(8).Cells(i + 10, 3) = i
Sheets(8).Cells(10, i + 3) = i
Next i
Sheets(8).Cells(10, N + 4) = N + 1
Sheets(8).Cells(11, 2).Select
End Sub