SOLUTION: Topic: Gauss-Jordan Elimination Method to solve linear equations (Matrices) Problem: -3x + 2y -6z = 6 5x + 7y -5z = 6 x + 4y -2z = 8 MY QUESTION: I am trying to set it u

Question 939300: Topic: Gauss-Jordan Elimination Method to solve linear equations (Matrices)
Problem:
-3x + 2y -6z = 6
5x + 7y -5z = 6
x + 4y -2z = 8
MY QUESTION: I am trying to set it up with excel solver. Not sure what to enter for "set objective".
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Result of solution using Gauss-Jordan elimination
Your matrix
x y z b
-3 2 -6 6
5 7 -5 6
1 4 -2 8

Find the pivot in the 1st column and swap the 3rd and the 1st rows
x y z b
1 4 -2 8
5 7 -5 6
-3 2 -6 6

Multiply the 1st row by 5
x y z b
5 20 -10 40
5 7 -5 6
-3 2 -6 6

Subtract the 1st row from the 2nd row and restore it
x y z b
1 4 -2 8
0 -13 5 -34
-3 2 -6 6

Multiply the 1st row by -3
x y z b
-3 -12 6 -24
0 -13 5 -34
-3 2 -6 6

Subtract the 1st row from the 3rd row and restore it
x y z b
1 4 -2 8
0 -13 5 -34
0 14 -12 30

Make the pivot in the 2nd column by dividing the 2nd row by -13
x y z b
1 4 -2 8
0 1 -5/13 34/13
0 14 -12 30

Multiply the 2nd row by 4
x y z b
1 4 -2 8
0 4 -20/13 136/13
0 14 -12 30

Subtract the 2nd row from the 1st row and restore it
x y z b
1 0 -6/13 -32/13
0 1 -5/13 34/13
0 14 -12 30

Multiply the 2nd row by 14
x y z b
1 0 -6/13 -32/13
0 14 -70/13 476/13
0 14 -12 30

Subtract the 2nd row from the 3rd row and restore it
x y z b
1 0 -6/13 -32/13
0 1 -5/13 34/13
0 0 -86/13 -86/13

Make the pivot in the 3rd column by dividing the 3rd row by -86/13
x y z b
1 0 -6/13 -32/13
0 1 -5/13 34/13
0 0 1 1

Multiply the 3rd row by -6/13
x y z b
1 0 -6/13 -32/13
0 1 -5/13 34/13
0 0 -6/13 -6/13

Subtract the 3rd row from the 1st row and restore it
x y z b
1 0 0 -2
0 1 -5/13 34/13
0 0 1 1

Multiply the 3rd row by -5/13
x y z b
1 0 0 -2
0 1 -5/13 34/13
0 0 -5/13 -5/13

Subtract the 3rd row from the 2nd row and restore it
x y z b
1 0 0 -2
0 1 0 3
0 0 1 1

Solution set:

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