diff --git a/Homework1/conjugate_gradient.py b/Homework1/conjugate_gradient.py
index 33e9d1e..99b0d4b 100644
--- a/Homework1/conjugate_gradient.py
+++ b/Homework1/conjugate_gradient.py
@@ -1,72 +1,83 @@
 import numpy as np
 import argparse
 import math
 
 # Arguments parser
 my_parser = argparse.ArgumentParser()
 my_parser.add_argument('-A', action='store', type=float, nargs='+', required=True, help='The matrix A in rowmajor format: numbers separated by space')
 my_parser.add_argument('-b', action='store', type=float, nargs='+', required=True, help='The vector b in rowmajor format: numbers separated by space')
 my_parser.add_argument('-x0', action='store', type=float, nargs='+', required=True, help='The initial guess x0 in rowmajor format: numbers separated by space')
 my_parser.add_argument('-Nmax', action='store', type=int,  default=20, help='Maximum number of iterations. Default: 20')
 my_parser.add_argument('-criteria', action='store', type=float, default=1e-6, help='Convergence criteria. Default: 1e-6')
 args = my_parser.parse_args()
 
 # Extracting matrix A, vector b, and the initial guess x0 from the input arguments
 A  = np.array(args.A)
 b  = np.array(args.b)
 x0 = np.array(args.x0)
 
 # Checking the compatibility of size of A with b (n: dimension of the problem)
 n=np.size(b)
 if np.size(A) != n*n:
     print('\n=====ERROR=====\n'
           'Matrix A and vector b are not compatible in size.\n'
           '===============\n')
     exit()
     
 # Checking the compatibility of size of x0 with A and b
 if np.size(x0) != n:
     print('\n=====ERROR=====\n'
           'Initial guess does not match to matrix A and vector b in size.\n'
           '===============\n')
     exit()
     
 # Converting matrix A from rowmajor to square form 
 A=A.reshape((n,n))
 
+# Converting A to the generalized form: (A+transpose(A))/2
+A=0.5*(A+np.transpose(A))
+
 # Converting optional settings from the arguments
 N_max=args.Nmax
 criteria=args.criteria
 
 # Iteration procedure
 step=0
 x=x0
 r=b-np.einsum('ij,j',A,x0)
 norm_residual=math.sqrt(np.einsum('j,j',r,r))
 p=r
 
 
 print('==========RESULT==========')
 while norm_residual>criteria and step<N_max:
     step = step+1
     
     alpha=np.einsum('j,j',r,r)/np.einsum('j,j',p,np.einsum('ij,j',A,p))    
     x=x+alpha*p
     
     r_backup=r
     p_backup=p
     
     r=r-alpha*np.einsum('ij,j',A,p)
     
     beta=np.einsum('j,j',r,r)/np.einsum('j,j',r_backup,r_backup)
     p=r+beta*p
     
     norm_residual=math.sqrt(np.einsum('j,j',r,r))
 
     print('step:      '+
           str(step)+'\n'+
           'residual:  '+
           str(norm_residual)+'\n'+
           'solution:  '+
           str(x)+
-          '\n--------------------------')
\ No newline at end of file
+          '\n--------------------------')
+    
+    
+    
+    
+    
+inv_A=np.linalg.inv(A)
+exact_sln=np.einsum('ij,j',inv_A,b)
+print(str(exact_sln)+'\n')
\ No newline at end of file