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.

dim(Nul(A)) is same as number of free variables

so, dim(Nul(A))=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.

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.

dim(Nul(A)) is same as number of free variables

so, dim(Nul(A))=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.