Gauss Jordan (RREF) elimination for \(Ax=0\) which has infinitely many solutions. Also known as non-trivial solutions.

So, the infinitely many solutions for \(Ax=0\) (Homogeneous system) are called nontrivial solutions.

❖ Solve a linear system \(Ax=0\) 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 infinitely many solutions.

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

\([A | b ]\) to \([\text{RREF} | 0 ]\)

We have done RREF for the augmented matrix \([ A | 0 ]\).

❖ 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 infinitely many solutions for \(Ax=0\) (Homogeneous system).