Gauss-Jordan Elimination Calculator
Solve systems of linear equations using Gauss-Jordan elimination. Enter the augmented matrix and get step-by-step solutions.
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How Gauss-Jordan Elimination Works
Gauss-Jordan elimination is a method for solving systems of linear equations by:
- Converting the augmented matrix to reduced row echelon form (RREF)
- Using elementary row operations:
- Swap rows
- Multiply a row by a non-zero scalar
- Add a multiple of one row to another
A matrix is in RREF when:
- All zero rows are at the bottom
- The leading coefficient of each non-zero row is 1
- The leading coefficient is the only non-zero entry in its column
- Leading coefficients move to the right as you go down the rows
Types of Solutions:
- Unique Solution: One solution exists
- No Solution: System is inconsistent
- Infinite Solutions: System has free variables