Gauss-Jordan Elimination
Calculate Gauss-Jordan Elimination instantly with the exact formula and a worked example.
Gauss-Jordan Elimination
a11
a12
a13
b1
a21
a22
a23
b2
a31
a32
a33
b3
x1
2
System
Unique solution
x2
3
x3
-1
det A
-1
rank A / rank [A|b]
3 / 3
More about: Gauss-Jordan Elimination
What it calculates
The “Gauss-Jordan Elimination” calculator computes x1 from 12 parameters: a11, a12, a13, b1, a21, a22, a23, b2, a31, a32, a33, b3.
A core calculation for studying, engineering tasks, and checking solutions.
Example calculation
With parameters a11 = 2, a12 = 1, a13 = -1, b1 = 8, a21 = -3, a22 = -1, a23 = 2, b2 = -11, a31 = -2, a32 = 1, a33 = 2, b3 = -3 the result is 2 (Equations: a11·x1 + a12·x2 + a13·x3 = b1, etc.; for a 2×2 system set a33 = 1 and a13, a23, a31, a32, b3 = 0).
How to use
- Enter a11, a12, a13, b1, a21, a22, a23, b2, a31, a32, a33 and b3 — each field above is adjustable with a slider.
- x1 is calculated automatically as you type.
- Check the worked example below to see the formula applied to real numbers.
- Copy the result or bookmark this calculator.
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FAQ
How is Gauss-Jordan Elimination calculated?
The Gauss-Jordan Elimination calculator computes x1 from a11, a12, a13, b1, a21, a22, a23, b2, a31, a32, a33, b3. Enter your values above and the exact formula is applied instantly; a worked example with real numbers is shown below.
Is the Gauss-Jordan Elimination calculator free?
Yes. It is completely free, needs no signup, runs entirely in your browser, and sends no data to any server.
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