Question 899715: Solve the system of linear equations using the Gauss-Jordan elimination method.
x + y + z = 0
2x − y + z = 1
x + y − 2z = 2
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 1,1,1,0
2,-1,1,1
1,1,-2,2
add down (-2) *row 1 to row 2
1,1,1,0
0,-3,-1,1
1,1,-2,2
add down (-1) *row 1 to row 3
1,1,1,0
0,-3,-1,1
0,0,-3,2
divide row 2 by -3
1,1,1,0
0,1,-1/-3,1/-3
0,0,-3,2
add down (0) *row 2 to row 3
1,1,1,0
0,1,1/3,1/-3
0,0,-3,2
divide row 3 by -3
1,1,1,0
0,1,1/3,1/-3
0,0,1,2/-3
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (-1/3) *row 3 to row 2
1,1,1,0
0,1,0,-3/27
0,0,1,2/-3
add up (-1) *row 3 to row 1
1,1,0,-2/-3
0,1,0,-1/9
0,0,1,2/-3
add up (-1) *row 2 to row 1
1,0,0,21/27
0,1,0,-1/9
0,0,1,2/-3
final
1,0,0,7/9
0,1,0,-1/9
0,0,1,2/-3
1,0,0,7/9 = 0.77777778
0,1,0,-1/9 = -0.11111111
0,0,1,-2/3 = -0.66666667
"7/9","-1/9","-2/3"
(7/9,-1/9,-2/3)
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