Gauss-Jordan Elimination is a method for solving a system of linear equations by transforming its augmented matrix into reduced row echelon form (RREF) using elementary row operations.

The Goal:

The objective is to manipulate the matrix until it looks like the identity matrix on the left side. The rightmost column will then contain the unique solution for each variable.

Allowed Row Operations:

• Swapping two rows: \( R_i \leftrightarrow R_j \)
• Multiplying a row by a non-zero scalar: \( R_i \rightarrow cR_i \)
• Adding a multiple of one row to another row: \( R_i \rightarrow R_i + cR_j \)

This calculator performs these steps systematically and shows you each operation, making the process easy to follow.