Solve the linear system:
x1 − 2x2 + x3 + 2x4 = −1,
2x1 − 4x2 + 2x3 + 4x4 = −2,
−x1 + 2x2 − x3 − 2x4 = 1,
3x1 − 6x2 + 3x3 + 6x4 = −3

and write the complete solution as x = xp + xn, a sum of particular solution plus a linear
combination of special solutions in the null space of the coefficient matrix.