random matrix A:
    -0.983     -0.521     -0.915     -0.586      -1.87      -1.25      -1.55 
     -1.54      -1.85    -0.0208      -1.67      -0.96    -0.0684      -1.13 
     -1.08      -1.88     -0.196     -0.358    -0.0638         -1      -1.22 
     -1.56      -1.08      -1.75     -0.684     -0.412      -1.89      -1.81 
     -1.62      -0.87      -1.03     -0.232     -0.572       -1.5      -1.91 
     -1.69       -1.9       -1.9    -0.0849      -1.13     -0.191      -1.97 
     -1.23      -1.38      -1.53      -1.42      -1.17     -0.631     -0.166 
random vector b:
    0.0354       0.41      0.553      0.236      0.703        0.1      0.291 
solution x to system A*x=b:
     -1.29     0.0282      0.443      0.522    -0.0852     -0.283      0.655 
check: A*x (should be equal b):
    0.0354       0.41      0.553      0.236      0.703        0.1      0.291 
test passed
A^-1*A=
         1          0  -2.22e-15   8.88e-16  -2.22e-16  -2.83e-15  -9.16e-16 
  6.11e-16          1   4.72e-16  -3.61e-16   8.33e-17   7.22e-16   6.77e-16 
  2.08e-16  -9.02e-17          1  -4.23e-16  -1.87e-16   1.32e-16  -2.04e-16 
  4.44e-16  -1.11e-16   4.44e-16          1  -3.33e-16   4.16e-16  -1.67e-16 
 -1.11e-16  -1.67e-16   1.67e-16   1.67e-16          1  -3.89e-16  -1.39e-17 
 -1.11e-16  -1.67e-16   5.55e-17  -2.22e-16   5.55e-17          1   1.04e-16 
  2.22e-16   2.22e-16   4.44e-16  -4.44e-16          0   9.99e-16          1 
A*A^-1=
         1  -2.22e-16   5.55e-17  -8.88e-16   8.88e-16  -1.11e-16   2.22e-16 
  3.89e-16          1   3.33e-16   2.22e-16  -1.11e-15  -1.11e-16  -2.22e-16 
  1.67e-16  -2.22e-16          1          0          0  -5.55e-17  -2.22e-16 
 -4.44e-16  -3.33e-16   1.67e-16          1   2.22e-16  -2.22e-16   4.44e-16 
         0   3.33e-16   5.55e-17          0          1          0  -4.44e-16 
 -5.55e-16          0   1.67e-16  -8.88e-16   8.88e-16          1          0 
  6.25e-17   1.53e-16   1.94e-16   -2.5e-16  -5.83e-16   6.94e-18          1