Gauss-Jordan Elimination Matrix Solver
What is Gauss-Jordan Elimination
Gauss-Jordan elimination is a systematic method for solving systems of linear equations by transforming them into a simpler equivalent form. This method extends the Gaussian elimination process by continuing until the coefficient matrix becomes a diagonal matrix, where each row represents a single variable.
The method works by performing a sequence of elementary row operations on the augmented matrix of the system until it reaches its reduced row echelon form (RREF). These operations include:
- Multiplying a row by a non-zero scalar
- Adding a multiple of one row to another row
- Swapping two rows
How to Use Gauss-Jordan Elimination Matrix Solver
Step 1: Select the size of your matrix using the dropdown menu. Choose between 2×2, 3×3, or 4×4 matrices depending on your system of equations.
Step 2: Enter the coefficients of your system of linear equations in the input fields. Each row represents one equation, and the last column represents the constants on the right-hand side of the equations.
Step 3: Verify that all coefficients are entered correctly. Use decimal points for non-integer values.
Step 4: Click the “Solve System” button to perform the Gauss-Jordan elimination.
Step 5: Review the step-by-step solution provided below the calculator. Each step shows the row operations performed and the resulting matrix transformation.
Step 6: Find your final solution at the bottom of the results section, where each variable’s value is clearly displayed.
Step 7: To solve another system, either click the “Clear” button to reset all fields or directly enter new values.