Question

Suppose you apply Gauss–Jordan elimination to a matrix. Explain how you can be sure that the resulting matrix is in reduced row-echelon form.

Short answer

The Gauss-Jordan technique is like the Gaussian elimination process, then again, actually the sections both above and below each of the pivot entry all terms will be zero.

Step-by-step solution

The Gauss-Jordan elimination

The Gauss-Jordan technique is like the Gaussian elimination process, then again, actually the sections both above and below each of the pivot entries all terms will be zero.

Subsequent to performing the Gaussian elimination process on a matrix, the outcome is in the row echelon structure, while the outcome after the Gauss-Jordan strategy is in the reduced row echelon structure.

Homogeneous system

A homogeneous linear system is generally always consistent because it will always be going to have a trivial solution.

In the event that a homogeneous linear system has something like one non-pivot column (for instance, the phase when it has a greater number of factors than conditions), then the system will be going to have an infinite number of solutions.

Linear systems that have the same type ofcoefficient matrix can also be solved simultaneously.

Hence, The Gauss-Jordan technique is like the Gaussian elimination process, then again, actually the sections both above and below each of the pivot entries all terms will be zero.