Question 895469: Solve by gauss elimination method 3x-y+2z=12,x+2y+3z=11,2x-2y-z=2
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 3x-y+2z=12,
x+2y+3z=11,
2x-2y-z=2
3,-1,2,12
1,2,3,11
2,-2,-1,2
divide row 1 by 3
1,-1/3,2/3,4
1,2,3,11
2,-2,-1,2
add down (-1) *row 1 to row 2
1,-1/3,2/3,4
0,7/3,7/3,7
2,-2,-1,2
add down (-2) *row 1 to row 3
1,-1/3,2/3,4
0,7/3,7/3,7
0,-4/3,-7/3,-6
divide row 2 by 7/3
1,-1/3,2/3,4
0,1,1,3
0,-4/3,-7/3,-6
add down (4/3) *row 2 to row 3
1,-1/3,2/3,4
0,1,1,3
0,0,-1,-2
divide row 3 by -1
1,-1/3,2/3,4
0,1,1,3
0,0,1,2
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (-1) *row 3 to row 2
1,-1/3,2/3,4
0,1,0,1
0,0,1,2
add up (-2/3) *row 3 to row 1
1,-3/9,0,8/3
0,1,0,1
0,0,1,2
add up (1/3) *row 2 to row 1
1,0,0,3
0,1,0,1
0,0,1,2
final
1,0,0,3
0,1,0,1
0,0,1,2
1,0,0,3
0,1,0,1
0,0,1,2
"3","1","2"
(3,1,2)
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