Gaussian Elimination Calculator: Solve Linear Systems Online

Solve Your System of Linear Equations

Select Matrix Size (N x N):

Enter Coefficients (A|b)

For a 2x2 system, fill rows 1 & 2. For 3x3, fill rows 1-3. For 4x4, fill all rows.

Quickly solve systems of linear equations using our Gaussian Elimination Calculator. Enter coefficients for 2x2, 3x3, or 4x4 matrices and get step-by-step solutions, including row operations and reduced row echelon form. Essential for students and professionals in linear algebra and numerical analysis.

Formula:

Gaussian Elimination transforms an augmented matrix [A|b] into row echelon form using elementary row operations to solve systems of linear equations. For a system of n equations and n variables:
a₁₁x₁ + a₁₂x₂ + ... + a_1nx_n = b₁
a₂₁x₁ + a₂₂x₂ + ... + a_2nx_n = b₂
...
a_n1x₁ + a_n2x₂ + ... + a_nnx_n = b_n
Here, a_ij are coefficients, x_i are variables, and b_i are constants.

Mathematics and Tools

Gaussian Elimination Calculator: Solve Linear Systems Online

Solve Your System of Linear Equations

Enter Coefficients (A|b)

Solution

Formula:

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