This can be considered as the continuation from the first one. This time, the Gauss-Jordan elimination is used. However, the full-fledged version of the elimination is not needed. This elimination comes into play due to the fact that if the elements in lower triangle of the matrix are all zeroes, the determinant is simply the product of the diagonals. This also applies in the upper triangle zeroes. It means: a ? ? ? a 0 0 0 0 b ? ? or ? b 0 0 's determinant = a*b*c*d 0 0 c ? ? ? c 0 0 0 0 d ? ? ? d ? = don't care. So, the elimination works to shape the matrix into one of these forms. My solution aims for the lower triangle zeroes. Full Gauss-Jordan elimination requires both upper and lower triangles be zeroes. I don't want to explain this in details as you can easily find it in good algebra books. I just give you a debug procedure "printarr", so that you can inject a line at mark {1} in order to learn how the algorithm works. If you'd like to have a more detailed look, put it at mark {2} instead. Try it using this matrix: 1 0 -1 0 0 3 0 2 -1 0 2 1 0 5 0 7 and then this one to understand when to "re-sort": 0 0 -1 0 0 3 0 2 -1 0 2 1 0 5 0 7 Here is my solution: ---------------------------------------------------- type { you can modify this dimension } arr = array[1..4, 1..4] of real; procedure printarr(new_a: arr; dim: integer); var i, j: integer; begin for i := 1 to dim do begin for j := 1 to dim do write(new_a[i,j]:5:3,' '); writeln; end; end; { Gauss-Jordan Elimination } function gauss(a: arr; dim: integer): real; var new_a : arr; i, j, k : integer; factor, temp, det : real; begin { copy the array } for i := 1 to dim do for j := 1 to dim do new_a[i,j] := a[i,j]; det := 1.0; { do the elimination } for i := 1 to dim-1 do begin { if the main diagonal value is zero } { re-sort the array } if (new_a[i,i] = 0) then begin for j := i+1 to dim do begin if (new_a[j,i] <> 0) then begin for k := 1 to dim do begin temp := new_a[i,k]; new_a[i,k] := new_a[j,k]; new_a[j,k] := temp; end; { For Gauss-Jordan Elimination, } { if we do a switch, the determinant } { switches sign. } det := -det; break; end; end; end; { if after the resorting, the value is still zero } { then the determinant is definitely zero } if (new_a[i,i] = 0) then begin gauss := 0; exit; end; { eliminate the lower rows to achieve triangular zeroes } for j := i+1 to dim do begin if (new_a[j,i] <> 0) then begin factor := (new_a[j,i] * 1.0) / new_a[i,i]; for k := i to dim do begin new_a[j,k] := new_a[j,k] - factor * new_a[i,k]; {2} end; {1} end; end; end; { calculate the main diagonal } for i := 1 to dim do det := det * new_a[i,i]; gauss := det; end; ----------------------------------------------------

Roby Joehanes, © 2001