Gauss Jordan elimination (RREF) for \(Ax=b\) which has a unique solution (only one 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 one solution (a unique solution).

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

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

(\(b\) 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 \(Ax=0\).