random matrix A:
    -0.547     -0.714      0.342      0.364     -0.239      0.713      0.238 
    -0.412      0.129     -0.101     -0.193      0.816     -0.175     -0.847 
    0.0237     -0.408      0.407      0.275     -0.193      0.913     -0.509 
     0.647     0.0739      0.264      0.108      0.807      0.568      0.346 
     0.233      0.822     -0.636     -0.903      0.177      0.916      0.241 
     0.441      0.238     -0.964    -0.0473      0.704     -0.262     -0.326 
    -0.666      0.816      -0.79     -0.648      0.909      0.679     -0.793 
random vector b:
     0.661      0.513    0.00975      0.827      0.902      0.926      0.403 
solution x to system A*x=b:
     0.421      -2.75     -0.719       -2.3       1.13      0.254      0.414 
check: A*x (should be equal b):
     0.661      0.513    0.00975      0.827      0.902      0.926      0.403 
test passed
A^-1*A=
         1  -1.11e-16  -1.11e-16          0          0  -2.22e-16  -2.22e-16 
  2.22e-16          1  -6.66e-16  -6.66e-16  -2.22e-16   4.44e-16   4.44e-16 
 -2.78e-16  -1.25e-16          1   8.33e-17   1.11e-16   6.94e-17   2.78e-17 
  2.22e-16   1.33e-15  -2.22e-16          1          0  -4.44e-16   4.44e-16 
 -2.71e-16  -1.25e-16   9.71e-17   3.47e-17          1    1.6e-16  -1.25e-16 
  1.11e-16   1.11e-16   5.55e-17  -8.33e-17  -5.55e-17          1   5.55e-17 
 -1.11e-16  -6.94e-18   5.55e-17  -6.94e-18   4.16e-17   4.16e-17          1 
A*A^-1=
         1   6.94e-16  -2.78e-17   1.25e-16  -1.73e-17  -2.05e-16  -4.27e-16 
  1.67e-16          1          0          0   9.02e-17   1.25e-16   -1.8e-16 
 -1.11e-16    2.5e-16          1          0   4.51e-17  -6.94e-17  -2.29e-16 
  2.78e-17  -1.11e-16   5.55e-17          1  -8.33e-17  -1.18e-16   2.05e-16 
   2.5e-16   2.78e-17   5.55e-17  -5.55e-17          1   2.39e-16  -7.81e-17 
 -1.94e-16  -4.16e-16          0  -6.94e-17  -2.43e-17          1   1.91e-16 
 -2.78e-16  -7.77e-16   1.11e-16          0   3.61e-16          0          1