Solve a system of linear equations using Gauss-Jordan elimination to reduced row-echelon form.
Gauss-Jordan elimination transforms the augmented matrix [A|b] into reduced row-echelon form (RREF) using partial pivoting. This directly yields the solution without back-substitution. The method handles any non-singular 3×3 system. Enter coefficients for the system a₁₁x₁ + a₁₂x₂ + a₁₃x₃ = b₁, etc.
Gauss-Jordan
[A|b] → [I|x] via row operations with partial pivoting
The calculator reports an error when the matrix is singular (determinant ≈ 0), indicating either no solution or infinitely many solutions.
Partial pivoting reduces numerical errors by choosing the largest available pivot element, preventing division by near-zero values.