Augmented Matrix Solver

All math tools

Solve systems of linear equations using augmented matrices and Gaussian elimination.

Matrix Coefficients

Solution Results

1.00

Variable 1 (x)

The values that satisfy all equations in the system.

Var 1 (x)1.00

Var 2 (y)2.00

About this calculator

What is an Augmented Matrix?

An augmented matrix is a matrix obtained by appending the columns of two matrices, typically for the purpose of performing the same elementary row operations on each. It is the primary tool for solving systems of linear equations using Gaussian elimination or Gauss-Jordan reduction.

💡

Pro Tips

The last column represents the constants on the right side of the equations.
A system can have exactly one solution, no solution (inconsistent), or infinitely many solutions (dependent).
Multiplying a row by a non-zero constant does not change the solution.

Fun Facts

"Gaussian elimination is named after Carl Friedrich Gauss, but it was used in China as early as 179 AD!"
"Computers use optimized versions of this algorithm to solve systems with millions of variables in engineering and weather forecasting."
"The number of variables you can solve for is limited by the number of independent equations you have."

Formula: Row Reduction (RREF)