Visual Tools
Calculators
Tables
Mathematical Keyboard
Converters
Other Tools

Gaussian Elimination Calculator

Solve Systems of Linear Equations

Matrix Size:
?Echelon Form requirements: 1. All rows consisting of only zeroes are at the bottom of the matrix 2. The leading entry (pivot) of a nonzero row is always strictly to the right of the leading entry of the row above it 3. All entries in a column below a leading entry are zeros
?Reduced Echelon Form requirements: 1. The matrix is in echelon form 2. The leading entry in each nonzero row is 1 (called a leading 1) 3. Each column containing a leading 1 has zeros in all its other entries (both above and below the leading 1)







About Matrix Equation Solving

Gaussian elimination is a powerful method for solving systems of linear equations and matrix equations. It is also known as row reduction or the echelon method. Our calculator can handle various tasks, including:

  • Solving matrix equations
  • Performing Gauss-Jordan elimination
  • Finding solutions to systems of linear equations
  • Converting matrices to row echelon form
  • Calculating inverse matrices (where applicable)

Whether you are a student learning linear algebra or a professional working with matrix calculations, our tool simplifies the process and provides clear, step-by-step explanations.