unit Unit3;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, Grids, StdCtrls;

const MaxDimension = 10;

type

  Vector = array[1..MaxDimension] of Double;
  Matrix = array[1..MaxDimension] of Vector;

  TForm3 = class(TForm)
    Label1: TLabel;
    Edit1: TEdit;
    StringGrid1: TStringGrid;
    StringGrid2: TStringGrid;
    Button1: TButton;
    Label2: TLabel;
    Label3: TLabel;
    ListBox1: TListBox;
    procedure Edit1Change(Sender: TObject);
    procedure Button1Click(Sender: TObject);
    procedure FormCreate(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form3: TForm3;

implementation

{$R *.dfm}

procedure TForm3.Button1Click(Sender: TObject);
  var a: Matrix;
      b,x: Vector;
      h: Double;
      i,j,k,n:integer;
begin
  //Ввод данных
  //Размерность системы
  n := StrToIntDef(Text, StringGrid1.ColCount);
  //Коэффициенты
  for j := 0 to n - 1 do
    for i := 0 to n - 1 do
      a[i + 1, j + 1] := StrToFloatDef(StringGrid1.Cells[j, i], 0);
  //Правая часть уравнения
  for I := 0 to n - 1 do b[i + 1] := StrToFloatDef(StringGrid2.Cells[0, i], 0);
  //Прямой ход - исключение переменных
  for i:=1 to n-1 do
    for j:=i+1 to n do
    begin
      a[j,i]:=-a[j,i]/a[i,i];
      for k:=i+1 to n do
        a[j,k]:=a[j,k]+a[j,i]*a[i,k];
        b[j]:=b[j]+a[j,i]*b[i]
    end;
    x[n]:=b[n]/a[n,n]; //Деление на ноль
    //Обратный ход - нахождение корней
    for i:=n-1 downto 1 do
    begin
      h:=b[i];
      for j:=i+1 to n do h:=h-x[j]*a[i,j];
      x[i]:=h/a[i,i]
    end;
    //Вывод результата
    for i:=1 to n do ListBox1.Items.Append('x(' + IntToStr(i) + ')=' + FloatToStr(x[i]));
end;

procedure TForm3.Edit1Change(Sender: TObject);
begin
  with StringGrid1, Edit1 do
  begin
    ColCount := StrToIntDef(Text, 3);
    RowCount := StrToIntDef(Text, 3);
  end;
  with StringGrid2, Edit1 do
    RowCount := StrToIntDef(Text, 3)
end;

procedure TForm3.FormCreate(Sender: TObject);
  var i, j: integer;
begin
  //Заполнить коэф уравнения
  Randomize;
  for I := 0 to StrToIntDef(Text, StringGrid1.ColCount) - 1 do
    for J := 0 to StrToIntDef(Text, StringGrid1.RowCount) - 1 do
      StringGrid1.Cells[I, J] := IntToStr(Random(100));
  for I := 0 to StrToIntDef(Text, StringGrid2.RowCount) - 1 do
    StringGrid2.Cells[0, I] := IntToStr(Random(100))
end;

end.