Kye

2020-12-15

Suppose a nonhomogeneous system of six linear equations in eight unknowns has a solution, with two free variables. Is it possible to change some constants on the equations’ right sides to make the new system inconsistent?

2k1enyvp

Skilled2020-12-16Added 94 answers

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.

so,

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

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.