diff --git a/functions/convert_matrix_to_triangular_matrix_gauss_naif.m b/functions/convert_matrix_to_triangular_matrix_gauss_naif.m
index ac8bb02..1940302 100644
--- a/functions/convert_matrix_to_triangular_matrix_gauss_naif.m
+++ b/functions/convert_matrix_to_triangular_matrix_gauss_naif.m
@@ -29,16 +29,28 @@ function [U,b] = convert_matrix_to_triangular_matrix_gauss_naif (U,b)
     else
            % convertiamo la matrice in una triangolare superiore
             for i=1:1:n-1
+                if U(i,i) == 0
+                      ok=0;
+                      break
+
+                end
                    for j=i+1:1:n
                         m= U(j,i) / U(i,i);
-                        U(j,:) =  U(j,:) + ( U(i,:) * (- m ) ) ; 
+                        U(j,i+1:n+1) =  U(j,i+1:n+1) + ( U(i,i+1:n+1) * (- m ) ) ; 
                         U(j,i)=m;
                    end
                 
             end
 
-            b=U(:,n+1);
-            U=U(:,1:n);
+            if ok == 0 || U(n,n)== 0
+                disp('impossibile convertire')
+                b=[];
+                U=[];
+            else
+            
+                b=U(:,n+1);
+                U=U(:,1:n);
+            end
     end
     
 end
diff --git a/functions/convert_matrix_to_triangular_matrix_gauss_pivoting.m b/functions/convert_matrix_to_triangular_matrix_gauss_pivoting.m
index c2a72a3..986dcfb 100644
--- a/functions/convert_matrix_to_triangular_matrix_gauss_pivoting.m
+++ b/functions/convert_matrix_to_triangular_matrix_gauss_pivoting.m
@@ -6,11 +6,13 @@
 %U=[10,20,30;1,5,3;4,56,34];  matrice di input
 %b=[1;2;17]; termini noti
 
-function [U,b] = convert_matrix_to_triangular_matrix_gauss_pivoting (U,b)
+function [U,b,pivot] = convert_matrix_to_triangular_matrix_gauss_pivoting (U,b)
 
 
     n= length(b); % lunghezza del vettore dei termini noti o numero equazioni
     U= [U,b]; % uniamo la matrice con la colonna dei termini noti
+    pivot = 1:1:n;
+    pivot = pivot';
 
     % convertiamo la matrice in una triangolare superiore
     for i=1:1:n-1
@@ -18,12 +20,17 @@ function [U,b] = convert_matrix_to_triangular_matrix_gauss_pivoting (U,b)
         if x_max == 0
             break
         else
+            %trovo gli indici di tutti i numeri uguali a max
             [x,y]= ind2sub(size(U),  find (abs(U(i:n,i)) == x_max) );
+            x=x(1);%prendo solo il primo indice
+            y=y(1);%prendo solo il primo indice
             x= x + i -1;
             y = i;
 
            if x~= i
                 U([i x],:) = U([x i],:);
+                pivot([i x]) = pivot([x i]);
+                
 
 
            end
@@ -31,7 +38,7 @@ function [U,b] = convert_matrix_to_triangular_matrix_gauss_pivoting (U,b)
            for j=i+1:1:n
 
                         m= U(j,i) / U(i,i);
-                        U(j,:) =  U(j,:) + ( U(i,:) * (- m ) ) ; 
+                        U(j,i+1:n+1) =  U(j,i+1:n+1) + ( U(i,i+1:n+1) * (- m ) ) ; 
                         U(j,i)=m;
 
            end
@@ -42,6 +49,7 @@ function [U,b] = convert_matrix_to_triangular_matrix_gauss_pivoting (U,b)
         disp('errore')
         b=[];
         U=[];
+        pivot = [];
     else
         b=U(:,n+1);
         U=U(:,1:n);
diff --git a/samples/sample_complete_liner_equation_system_resolve.m b/samples/sample_complete_liner_equation_system_resolve.m
index 2a3c93d..0372e5c 100644
--- a/samples/sample_complete_liner_equation_system_resolve.m
+++ b/samples/sample_complete_liner_equation_system_resolve.m
@@ -2,10 +2,10 @@
 % in matrice triangolare superiore con gauss pivoting parziale
 % e algoritmo di bottom up con sostituzione
 
-U=[4,8,12,16;2,9,6,8;0,1,1,4;6,2,2,4]; % matrice di input
-b=[1;-1;2;1]; %termini noti
 
-[x,y] = convert_matrix_to_triangular_matrix_gauss_pivoting(U,b);
-[x1] = linear_system_resolver_triangular_matrix(x,y);
-x1
+U=[2,4,-2;1,-1,5;4,1,-2] % matrice di input
+b=[6;-3;-10] %termini noti
+
+[x,y,z] = convert_matrix_to_triangular_matrix_gauss_pivoting(U,b)
+[x1] = linear_system_resolver_triangular_matrix(x,y)