Row-reduce any matrix to echelon and reduced row-echelon form with pivot tracking.
Gaussian elimination transforms a matrix into reduced row echelon form (RREF) using elementary row operations: swapping rows, scaling rows, and adding multiples of one row to another. Partial pivoting is used for numerical stability. The pivot columns identify the linearly independent columns.
Row Operations
R_i ← R_i − (R_i[k]/R_pivot[k]) × R_pivot
Row Echelon Form has leading 1s with zeros below each pivot. Reduced Row Echelon Form additionally has zeros above each pivot, making the solution directly readable.
Yes. Enter the augmented matrix [A|b] where the last column is the constants vector. After RREF, the solution is directly readable from the last column.