Gauss-Jordan Elimination 2×2 Calculator
Result
Gauss-Jordan Elimination 2×2 Calculator — dedicated 2×2 method with domain checks.
Formula
- Gauss-Jordan Elimination 2×2 Calculator. Reduce the augmented matrix [[a,b,c],[d,e,f]] by pivot normalization and row elimination to RREF [[1,0,x],[0,1,y]] for a unique solution. This two-equation solver handles only unique solutions and rejects singular (non-unique or inconsistent) systems. The calculator reports an explicit result within this documented 2×2 scope.
- The main inputs are a, b, c, d, e, f. Enter them in the units and format shown in the calculator.
- Keep comparable quantities in compatible units whenever the formula combines or compares them.
- Changing any input above recalculates the result with the same calculation engine used by this page.
Example: Gauss-Jordan Elimination 2×2
- a: 2
- b: 1
- c: 5
- d: 1
- e: -1
- f: 1
For 2x+y=5 and x−y=1, Gauss-Jordan reduction yields RREF [[1,0,2],[0,1,1]], giving x=2 and y=1.
Sample result: Calculating…
Frequently asked questions
What does the Gauss-Jordan Elimination 2×2 calculate?
Gauss-Jordan Elimination 2×2 Calculator — dedicated 2×2 method with domain checks.
Which values should I enter?
Enter a, b, c, d, e, f using the units and format shown beside each field.
What formula does this calculator use?
The calculator uses the following relationship: Reduce the augmented matrix [[a,b,c],[d,e,f]] by pivot normalization and row elimination to RREF [[1,0,x],[0,1,y]] for a unique solution. This two-equation solver handles only unique solutions and rejects singular (non-unique or inconsistent) systems..
Why might my result differ from another source?
Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.
Does the result update automatically?
Yes. Changing an input updates the result using the same calculation engine shown on this page.