Gauss-Jordan Elimination Calculator

Your details

Choose how many equations and unknowns your system has.
Coefficient of x in equation 1.
Coefficient of y in equation 1.
Coefficient of z in equation 1.
Right-hand side constant of equation 1.
Coefficient of x in equation 2.
Coefficient of y in equation 2.
Coefficient of z in equation 2.
Right-hand side constant of equation 2.
Coefficient of x in equation 3.
Coefficient of y in equation 3.
Coefficient of z in equation 3.
Right-hand side constant of equation 3.
x
2

Value of the first unknown x

y3
z-1
Rank of A3
Nullity0
Solution typeUnique solution
RREF matrix[ 1 0 0 | 2 ]; [ 0 1 0 | 3 ]; [ 0 0 1 | -1 ]
Rank3
Nullity0

Unique solution

  • Unique solution: x = 2, y = 3, z = -1.
  • Rank = 3 (equals n = 3), so the coefficient matrix is invertible.
  • The RREF is the unique canonical form of the augmented matrix - it makes the solution or its absence immediately visible.

Next stepVerify by substituting the solution back into each original equation.

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