Titlu

 A = {{2, 1, 1, 3, 2}, {1, 2, 2, 1, 1}, {1, 2, 9, 1, 5}, {3, 1,
     1, 7, 1}, {2, 1, 5, 1, 8}};

MatrixForm[A]
 L = U = Table[0, {i, 1, 5}, {j, 1, 5}];

 Doolittle[A_] := {
  n = Length[A];
  For[k = 1, k <= n , k++,
   L[[k, k]] = 1;
   For[j = k, j <= n, j++,
    U[[k, j]] = A[[k, j]] - Sum[L[[k, m]]*U[[m, j]], {m, 1, k - 1}]
    ];
   For[i = k + 1, i <= n, i++,
    L[[i,
       k]] = (A[[i, k]] - Sum[L[[i, m]]* U[[m, k]], {m, 1, k - 1}])/
      U[[k, k]]];
    ]
     }


Doolittle[A];
MatrixForm[A]
MatrixForm[L.U]