Gaussian Elimination Solver

Row echelon Ax=b

System

rank = 3 / 3

Solution x

(2.000000, 3.000000, -1.000000)

Row Operations

Augmented [A|b]

2.000  1.000  -1.000  8.000
-3.000  -1.000  2.000  -11.000
-2.000  1.000  2.000  -3.000

Swap R1 ↔ R2

-3.000  -1.000  2.000  -11.000
2.000  1.000  -1.000  8.000
-2.000  1.000  2.000  -3.000

R2 -= -0.667·R1

-3.000  -1.000  2.000  -11.000
0.000  0.333  0.333  0.667
-2.000  1.000  2.000  -3.000

R3 -= 0.667·R1

-3.000  -1.000  2.000  -11.000
0.000  0.333  0.333  0.667
0.000  1.667  0.667  4.333

Swap R2 ↔ R3

-3.000  -1.000  2.000  -11.000
0.000  1.667  0.667  4.333
0.000  0.333  0.333  0.667

R3 -= 0.200·R2

-3.000  -1.000  2.000  -11.000
0.000  1.667  0.667  4.333
0.000  0.000  0.200  -0.200

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About Gaussian Elimination Solver

A Gaussian elimination solver for linear systems Ax=b. Performs row operations to reach row echelon form, then back-substitutes. Shows each row operation step-by-step. Detects rank, inconsistency, and free variables. Select from preset systems. All calculations are client-side.

Gaussian Elimination Solver Features

Row echelon
Back sub
Step display
Rank
Presets

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