```PROGRAM Hilbert;
{ solution by Gauss-Jordan elimination }
{ From Borland Pascal Programs for Scientists and Engineers }
{ by Alan R. Miller, Copyright C 1993, SYBEX Inc }
{ N x N inverse Hilbert matrix }
{ solution is 1 1 1 1 1 }
USES WinCrt;  { Crt for non-windows version}

CONST
Maxr = 11;  Maxc = 11;

TYPE
FltPt = Real;  { or Double }
Arys  = ARRAY[1..Maxc] OF FltPt;
Ary2s = ARRAY[1..Maxr, 1..Maxc] OF FltPt;

VAR
Y, Coef: Arys;
A, B: Ary2s;
N, M, I, J: Integer;
Error: Boolean;

PROCEDURE Get_Data(VAR A: Ary2s;
VAR Y: Arys;
VAR N, M: Integer);
{ Setup N-by-N hilbert matrix }
VAR
I, J: Integer;

BEGIN
FOR I := 1 TO N-1 DO
BEGIN
A[N,I] := 1.0/(N + I - 1);
A[I,N] := A[N,I]
END;
A[N,N] := 1.0/(2*N -1);
FOR I := 1 TO N DO
BEGIN
Y[I] := 0.0;
FOR J := 1 TO N DO
Y[I] := Y[I] + A[I,J]
END;
WriteLn;
IF N < 7 THEN
BEGIN
FOR I:= 1 TO N  DO
BEGIN
FOR J:= 1 TO M DO Write(A[I,J]:7:5, '  ');
WriteLn(' : ', Y[I]:7:5)
END;
WriteLn
END  { if N<7 }
END; { procedure Get_Data }

PROCEDURE Write_Data;
{ print out the answers }
VAR
I: Integer;

BEGIN
WriteLn(' Solution for', M:3, ' equations');
IF M > 6 THEN
BEGIN
FOR I := 1 TO 6 DO Write(Coef[I]:11:7);
Writeln;
FOR I := 7 TO M DO Write(Coef[I]:11:7)
END
ELSE
FOR I := 1 TO M DO Write(Coef[I]:11:7);
WriteLn;
END; { Write_Data }

{\$I GAUSSJ} {Listing 4.4}

BEGIN  { main program }
A[1,1] := 1.0;
N := 2; M := N;
REPEAT
Get_Data(A, Y, N, M);
FOR I := 1 TO N DO
FOR J := 1 TO N DO
B[I,J] := A[I,J]; { Setup work array }
Gaussj(B, Y, Coef, N, Error);
IF NOT Error THEN Write_Data;
N := N+1;  M := N
UNTIL N > Maxr;
Writeln; Writeln('  Press Enter to end');
REPEAT UNTIL KeyPressed;
DoneWinCrt  { for Windows version only }
END.

```