n=4

It shows that the basic solution system of homogeneous linear equations Ax=0 has only one solution vector.

According to the meaning of the question,

Aη 1=b

A(2η2-3η3)=-b

∴A(η 1+2η2-3η3)=0

∴η 1+2η2-3η3 is the solution vector of Ax=0.

η 1+2η2-3η3=( 1,3,2,4)^t

Nonzero vector,

∴Ax=0, the solution vector in the basic solution system is

( 1,3,2,4)^T

According to the structure of solutions of nonhomogeneous linear equations,

The general solution of Ax=b is

x = k( 1,3,2,4)^t+( 1,2,3,4)^t

(k is an arbitrary constant)