Matrix:

Row   Column       Value
---   ------       -----
  1        1    3.00e+00
  1        2    2.00e+00
  1        3   -1.00e+00
  2        1    2.00e+00
  2        2   -2.00e+00
  2        3    4.00e+00
  3        1   -1.00e+00
  3        2    5.00e-01
  3        3   -1.00e+00

Right-hand-side vector:

i = 0  rhs[i] = 1
i = 1  rhs[i] = -2
i = 2  rhs[i] = 0

Solution vector:

i = 0  a_sol[i] = 1.0000000000e+00
i = 1  a_sol[i] = -2.0000000000e+00
i = 2  a_sol[i] = -2.0000000000e+00

Matrix times solution vector vs. rhs vector:

i = 0  matrix * a_sol[i] = 1.000000  rhs[i] = 1.000000
i = 1  matrix * a_sol[i] = -2.000000  rhs[i] = -2.000000
i = 2  matrix * a_sol[i] = 0.000000  rhs[i] = 0.000000