Gauss Jordan (RREF) elimination for Ax=0, infinitely many solutions
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 [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).
The link to this playlist (Linear Algebra):
• Linear Algebra
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