RREF Calculator

Calculate Row Reduced Echelon Form of matrices

Matrix Input

Solution Steps

Understanding RREF

Row Reduced Echelon Form (RREF) is a standardized form of a matrix that makes it easier to solve systems of linear equations and understand the relationships between variables.

Properties of RREF

  • • Leading 1 in each non-zero row
  • • All entries above and below leading 1s are 0
  • • Each leading 1 is the only nonzero entry in its column
  • • All zero rows are at the bottom

Applications

  • • Solving linear equations
  • • Finding matrix rank
  • • Determining linear independence
  • • Computing matrix inverse

Matrix Operations

Elementary Row Operations

  • • Swap two rows
  • • Multiply row by scalar
  • • Add multiple of one row to another

Matrix Properties

  • • Rank
  • • Linear independence
  • • Solution existence
  • • Solution uniqueness

System Analysis

  • • Consistent vs inconsistent
  • • Unique vs infinite solutions
  • • Free variables
  • • Parameter relationships