Question 912871: solve equations by jauss jordan method,2x+y-z=4,3x+5y+z=16,x-2y-5z=3 (by row operation)
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 2x+y-z=4,
3x+5y+z=16,
x-2y-5z=3
2,1,-1,4
3,5,1,16
1,-2,-5,3
divide row 1 by 2
1,1/2,-1/2,2
3,5,1,16
1,-2,-5,3
add down (-3) *row 1 to row 2
1,1/2,-1/2,2
0,7/2,5/2,10
1,-2,-5,3
add down (-1) *row 1 to row 3
1,1/2,-1/2,2
0,7/2,5/2,10
0,-5/2,-9/2,1
divide row 2 by 7/2
1,1/2,-1/2,2
0,1,10/14,20/7
0,-5/2,-9/2,1
add down (5/2) *row 2 to row 3
1,1/2,-1/2,2
0,1,5/7,20/7
0,0,-76/28,114/14
divide row 3 by -19/7
1,1/2,-1/2,2
0,1,5/7,20/7
0,0,1,-3
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (-5/7) *row 3 to row 2
1,1/2,-1/2,2
0,1,0,5
0,0,1,-3
add up (1/2) *row 3 to row 1
1,2/4,0,1/2
0,1,0,5
0,0,1,-3
add up (-1/2) *row 2 to row 1
1,0,0,-2
0,1,0,5
0,0,1,-3
final
1,0,0,-2
0,1,0,5
0,0,1,-3
"-2","5","-3"
(-2,5,-3)
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