It can be seen from the rank of 5*4 matrix A that the dimension of the solution space is 1 (the number of matrix columns-rank).

So we just need to get the general solution of the homogeneous equation Ax=0 and the special solution of the nonhomogeneous equation Ax=b, and just combine them.

Because N 1, N2 and N3 are three different solution vectors of the nonhomogeneous linear equations Ax=b, we can get:

A(n 1+N2+2n 3)= A(3n 1+N2)= 4b；

Choose one, and get a special case of non-homogeneous equation (1/2,0,0).

Therefore: a (n1+N2+2n3-(3n1+N2) = 0;

The general solution k (0,4,6,8) of homogeneous equation is obtained.

So the general solution can be written as k (0 0,4,6,8)+(1/2,0,0).