SOLUTION: Use Gauss-Jordan elimination to solve the following system of equations.
x+y+z=2
2x-3y+z=-11
-x+2y-z=8
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Question 958270: Use Gauss-Jordan elimination to solve the following system of equations.
x+y+z=2
2x-3y+z=-11
-x+2y-z=8
Found 2 solutions by MathLover1, LinnW:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Your matrix
Find the pivot in the 1st column in the 1st row
Eliminate the 1st column
Make the pivot in the 2nd column by dividing the 2nd row by -5
Eliminate the 2nd column
Make the pivot in the 3rd column by dividing the 3rd row by
Eliminate the 3rd column
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
The beginning matrix is
1 1 1 2
2 -3 1 -11
-1 2 -1 8
add 1 times the 1st row to the 3rd row
1 1 1 2
2 -3 1 -11
0 3 0 10
add -2 times the 1st row to the 2nd row
1 1 1 2
2 -5 -1 -15
0 3 0 10
add 3/5 times the 2nd row to the 3rd row
1 1 1 2
0 -5 -1 -15
0 0 -3/5 1
multiply the 3rd row by -5/3
1 1 1 2
0 -5 -1 -15
0 0 1 -5/3
add -1 times the 3rd row to the 1st row
1 1 0 11/3
0 -5 -1 -15
0 0 1 -5/3
add -1 times the 3rd row to the 2nd row
1 1 0 11/3
0 -5 0 -50/3
0 0 1 -5/3
multiply the 2nd row by -1/5
1 1 0 11/3
0 -5 0 -50/3
0 0 1 -5/3
add 1 times the 3rd row to the 2nd row
1 1 0 11/3
0 1 0 10/3
0 0 1 -5/3
add -1 times the 2nd row to the 1st row
1 0 0 1/3
0 1 0 10/3
0 0 1 -5/3
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