Row Echelon Form Calculator

Transform matrices to Row Echelon Form with ease. Solve systems of linear equations quickly and understand the process visually.

Number of Equations

Choose the number of equations for your system.

Equation 1:

x +

y =

Constant

Equation 2:

x +

y =

Constant

Equation 3:

x +

y =

Constant

Understanding Row Echelon Form

The Row Echelon Form (REF) is a simplified form of a matrix achieved through Gaussian elimination. It's crucial for solving systems of linear equations, finding matrix ranks, and computing determinants.

A matrix is in Row Echelon Form if:

All non-zero rows are above any rows of all zeros.
The leading entry (pivot) of a non-zero row is always strictly to the right of the leading entry of the row above it.
All entries in a column below a leading entry are zeros.

This calculator helps you convert any given matrix into its Row Echelon Form. Simply input the coefficients of your linear equations, and the tool will perform Gaussian elimination to provide you with the REF and the solution to the system, if one exists.

For example, consider a system of equations:

2x - y = 1
x + y = 5

Inputting the coefficients into the calculator will transform the corresponding matrix into Row Echelon Form, making it easier to solve for x and y.

Further reading on Row Echelon Form: Wikipedia.