Eigenvalues & eigenvectors
Real or complex eigenpairs with residual checks.
Open calculatorMathematics / Free calculator
Gaussian elimination / RREF
Reduce a matrix to reduced row echelon form using exact rational arithmetic, with a complete row-operation trace.
01 Your inputs
02 Your result
Enter your values and select Calculate.
The method
A worked example
The augmented matrix [1 2 5; 3 4 11] reduces to [1 0 1; 0 1 2]. Interpreted as x + 2y = 5 and 3x + 4y = 11, this gives x = 1 and y = 2. Substitution confirms both equations.
Assumptions & limits
Supports 1–7 rows and 1–7 columns with exact integers, finite decimals, or fractions. Scientific notation exponents are limited to ±15. Rational numerators and denominators are capped below 260 digits. Rank refers to the entire supplied matrix, including any augmented column.
Calculation source: Selected exact rational and row-reduction functions from Math Workbench beta 0.5.