1. What is Gauss-Jordan Elimination?

Gauss-Jordan elimination is an algorithm for solving systems of linear equations. It transforms the augmented matrix [A|b] into reduced row echelon form (RREF) to find the solution to Ax = b.

2. How Does the Calculator Work?

The calculator performs the following operations:

The process involves:

• Swapping rows
• Multiplying rows by non-zero scalars
• Adding multiples of rows to other rows

3. Steps in Gauss-Jordan Elimination

Details: The method systematically eliminates variables to transform the matrix into reduced row echelon form where the solution can be read directly.

4. Using the Calculator

Tips: Enter the augmented matrix in the format [[a11,a12,...|b1],[a21,a22,...|b2],...]. Separate elements with commas and rows with semicolons.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Gaussian and Gauss-Jordan elimination?
A: Gaussian elimination produces row echelon form, while Gauss-Jordan continues to reduced row echelon form.

Q2: When does the method fail?
A: When the system is inconsistent (no solution) or when the matrix is singular (infinite solutions).

Q3: Can this solve any linear system?
A: Yes, for any m×n system, though some may have no or infinite solutions.

Q4: How is this related to matrix inversion?
A: The same method can invert matrices by augmenting with the identity matrix.

Q5: What's the computational complexity?
A: O(n³) for an n×n system, making it practical for small to medium systems.