Step 1

According to the given information, a non-homogeneous system of six linear equations in eight unknown has a solution with two free variables.

It is required to check whether is it possible to change some constants on the equations on right side to make new system inconsistence.

\(\displaystyle\dim{\left({N}\underline{{{A}}}\right)}\) is same as number of free variables

so, \(\displaystyle\dim{\left({N}\underline{{{A}}}\right)}={2}\)

Step 2

Since, n = 8 as system has eight unknowns so, rank of coefficient matrix is:

rank(A)=8-2=6

Step 3

Further, col(A) is a six-dimensional subspace of \(\displaystyle{R}^{{6}}\) because it has six linear equations so, \(\displaystyle{c}{o}{l}{\left({A}\right)}={R}^{{6}}\)

This means that Ax = b has a solution for every b and cannot change constant on right side to make system inconsistence.

Hence, it is not possible to change the constants.