System of Equations (3×3)

Gaussian elimination for three unknowns

1x + 1y + 1z = 6
1x + 2y + 3z = 14
2x + 3y + 1z = 11
Solution type
Unique solution
x
1
y
2
z
3
Determinant of A
-3
Augmented matrix reduced by Gaussian eliminationThe augmented matrix [A | b] is row-reduced to the identity, and the last column reads off the unique solution. Solution: x = 1, y = 2, z = 3.Augmented matrix [A | b]11161231423111Gaussian eliminationReduced row-echelon form100101020013