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Mathematik und Algebra
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System of Equations (3×3)
System of Equations (3×3)
Gaussian elimination for three unknowns
Favorit
Drucken
coefficient of x (Equation 1)
x +
coefficient of y (Equation 1)
y +
coefficient of z (Equation 1)
z
=
right-hand side (Equation 1)
coefficient of x (Equation 2)
x +
coefficient of y (Equation 2)
y +
coefficient of z (Equation 2)
z
=
right-hand side (Equation 2)
coefficient of x (Equation 3)
x +
coefficient of y (Equation 3)
y +
coefficient of z (Equation 3)
z
=
right-hand side (Equation 3)
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
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Augmented matrix reduced by Gaussian elimination
The 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]
1
1
1
6
1
2
3
14
2
3
1
11
Gaussian elimination
Reduced row-echelon form
1
0
0
1
0
1
0
2
0
0
1
3
