Question 901414: Solve the system of linear equations using the Gauss-Jordan elimination method.
− x2 + x3 = 1
4x1 − 3x2 + 2x3 = 18
3x1 + 2x2 + x3 = 13
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 0x-y+z=1
4x-3y+2z=18
3x+2y+z=13
4x-3y+2z=18
0x-y+z=1
3x+2y+z=13
4,-3,2,18
0,-1,1,1
3,2,1,13
divide row 1 by 4
1,-3/4,2/4,18/4
0,-1,1,1
3,2,1,13
add down (0) *row 1 to row 2
1,-3/4,1/2,9/2
0,-1,1,1
3,2,1,13
add down (-3) *row 1 to row 3
1,-3/4,1/2,9/2
0,-1,1,1
0,17/4,-1/2,-1/2
divide row 2 by -1
1,-3/4,1/2,9/2
0,1,-1,-1
0,17/4,-1/2,-1/2
add down (-17/4) *row 2 to row 3
1,-3/4,1/2,9/2
0,1,-1,-1
0,0,30/8,30/8
divide row 3 by 15/4
1,-3/4,1/2,9/2
0,1,-1,-1
0,0,1,1
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,-3/4,1/2,9/2
0,1,0,0
0,0,1,1
add up (-1/2) *row 3 to row 1
1,-6/8,0,4
0,1,0,0
0,0,1,1
add up (3/4) *row 2 to row 1
1,0,0,4
0,1,0,0
0,0,1,1
final
1,0,0,4
0,1,0,0
0,0,1,1
"4","0","1"
(4,0,1)
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