Work out reduced row echelon form instantly with clear inputs, formula shown and shareable results.
Reduced row echelon form goes further than plain echelon form: each pivot is 1 and every other entry in its column is 0. For an augmented system the last column then reads off the solution directly.
Consistency
solvable ⇔ rank of the augmented matrix equals rank of the coefficient matrix
It reduces to the identity, giving x₁ = 2, x₂ = 3, x₃ = −1.
A row of zeros with a non-zero constant means 0 = c, which is impossible, and shows up as the augmented rank exceeding the coefficient rank.