Gauss Elimination Method
The objective of gauss elimination method is to transform the system of equation to a new having an upper triangular form which back substitution scheme is used to obtain the component of x
Ex.
X1 – X2 + X3 – X4 = 1
2X1 – X2 + 3X3 + X4 = 2
X1 + X2 + 2X3 + 2X4 = 3
X1 + X2 + X3 + X4 = 3
Solution
Ex.
X1 – X2 + X3 – X4 = 1
2X1 – X2 + 3X3 + X4 = 2
X1 + X2 + 2X3 + 2X4 = 3
X1 + X2 + X3 + X4 = 3
Solution
2X4 = -2 -X3 – 3X4 = 2 X2 + X3 + 3X4 = 0 X1 – X2 + X3 –X4 = 1
X4 = -1 -X3 + 3 = 2 X2 + 1 – 3 = 0 X1 – 2 + 1 + 1 = 1
X3 = 1 X2 = 2 X1 = 1
X4 = -1 -X3 + 3 = 2 X2 + 1 – 3 = 0 X1 – 2 + 1 + 1 = 1
X3 = 1 X2 = 2 X1 = 1