import numpy as np

A = np.matrix( '-2,  2, -5, -7;\
                 2, -3,  7, 11;\
                -4,  3, -7, -9' )

print( 'A = ' )
print( A )

G0 = np.matrix( ' 1,  0,  0;\
                  1,  1,  0;\
                 -2,  0,  1' );

A0 = G0 * A

print( 'A0 = ' )
print( A0 )

print( 'A0 =' )
print( A0 )

G1 = np.matrix( ' 1,  2,  0;\
                  0,  1,  0;\
                  0, -1,  1' );

A1 = G1 * A0

print( 'A1 = ' )
print( A1 )

print( 'A1 =' )
print( A1 )

G2 = np.matrix( ' 1,  0,  1;\
                  0,  1, -2;\
                  0,  0,  1' );

A2 = G2 * A1

print( 'A2 = ' )
print( A2 )

print( 'A2 =' )
print( A2 )

D = np.matrix( '-0.5,  0,  0;\
                  0,  -1,  0;\
                  0,  0,   1' );

A3 = D * A2

print( 'A3 = ' )
print( A3 )

A = np.matrix( '-2,  2, -5;\
                 2, -3,  7;\
                -4,  3, -7' )

print( 'A = ' )
print( A )

x = np.matrix( '-1;\
                -2;\
                 1' )

print( 'x = ' )
print( x )

print( ' A * x = ' )
print( A * x )