Question 1163482: Solve the following system of equations by Gauss elimination method :
x + 2y + z = 2 , 3x + y - 2z = 1 , 4x - 3y - z = 3
Answer by ikleyn(52775)   (Show Source):
You can put this solution on YOUR website! .
x + 2y + z = 2
3x + y - 2z = 1
4x - 3y - z = 3
Your augmented matrix
X1 X2 X3 b
1 1 2 1 2
2 3 1 -2 1
3 4 -3 -1 3
Find the pivot in the 1st column in the 1st row
X1 X2 X3 b
1 1 2 1 2
2 3 1 -2 1
3 4 -3 -1 3
Multiply the 1st row by 3
X1 X2 X3 b
1 3 6 3 6
2 3 1 -2 1
3 4 -3 -1 3
Subtract the 1st row from the 2nd row and restore it
X1 X2 X3 b
1 1 2 1 2
2 0 -5 -5 -5
3 4 -3 -1 3
Multiply the 1st row by 4
X1 X2 X3 b
1 4 8 4 8
2 0 -5 -5 -5
3 4 -3 -1 3
Subtract the 1st row from the 3rd row and restore it
X1 X2 X3 b
1 1 2 1 2
2 0 -5 -5 -5
3 0 -11 -5 -5
Make the pivot in the 2nd column by dividing the 2nd row by -5
X1 X2 X3 b
1 1 2 1 2
2 0 1 1 1
3 0 -11 -5 -5
Multiply the 2nd row by 2
X1 X2 X3 b
1 1 2 1 2
2 0 2 2 2
3 0 -11 -5 -5
Subtract the 2nd row from the 1st row and restore it
X1 X2 X3 b
1 1 0 -1 0
2 0 1 1 1
3 0 -11 -5 -5
Multiply the 2nd row by -11
X1 X2 X3 b
1 1 0 -1 0
2 0 -11 -11 -11
3 0 -11 -5 -5
Subtract the 2nd row from the 3rd row and restore it
X1 X2 X3 b
1 1 0 -1 0
2 0 1 1 1
3 0 0 6 6
Make the pivot in the 3rd column by dividing the 3rd row by 6
X1 X2 X3 b
1 1 0 -1 0
2 0 1 1 1
3 0 0 1 1
Multiply the 3rd row by -1
X1 X2 X3 b
1 1 0 -1 0
2 0 1 1 1
3 0 0 -1 -1
Subtract the 3rd row from the 1st row
X1 X2 X3 b
1 1 0 0 1
2 0 1 1 1
3 0 0 -1 -1
Multiply the 3rd row by -1
X1 X2 X3 b
1 1 0 0 1
2 0 1 1 1
3 0 0 1 1
Subtract the 3rd row from the 2nd row and restore it
X1 X2 X3 b
1 1 0 0 1
2 0 1 0 0
3 0 0 1 1
ANSWER. The solution is (x,y,z) = (1,0,1).
Solved.
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