Gauss Jordan (RREF) elimination for Nonhomogeneous system \(Ax=b\) which has No solution.

❖ Solve a linear system \(Ax=b\) by using a Reduced Row Echelon Form (RREF).

(Sometimes, they called this method as Gauss Jordan elimination ( or Gauss-Jordan reduction) method). In this example, the answer to this system has No solution.

❖ The method can process for \(Ax=b\) as the following

\([A | b ]\) to \([\text{RREF} | c ]\)

So,

(\(b\) vector) changed to (\(c\) vector) because we have done RREF for the augmented matrix \([ A | b ]\), so the answer is the vector \(c\).

❖ Previously in this playlist, we have mentioned the steps to determine if a matrix is reduced row echelon form (RREF) or not.

Here, we have explained a unique solution (one solution) for the Nonhomogeneous system \(Ax=b\).

Later, we will talk about the Homogeneous system \(Ax=0\).