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