SOLUTION: Solve by using the Gauss-Jordan elimination method: x+y-z=2 2x+3y-z=7 3x-2y+z=9 I know that you have to convert them to 1 0 0 | 2 0 1 0 | 7 0 0 1 | 9 I am just n

Algebra ->  Algebra  -> Matrices-and-determiminant -> SOLUTION: Solve by using the Gauss-Jordan elimination method: x+y-z=2 2x+3y-z=7 3x-2y+z=9 I know that you have to convert them to 1 0 0 | 2 0 1 0 | 7 0 0 1 | 9 I am just n      Log On

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Question 102522: Solve by using the Gauss-Jordan elimination method:
x+y-z=2
2x+3y-z=7
3x-2y+z=9
I know that you have to convert them to
1 0 0 | 2
0 1 0 | 7
0 0 1 | 9
I am just not clear on how to do this row by row.
Any help would be greatly appreciated.
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given matrix:


%28matrix%283%2C4%2C1%2C1%2C-1%2C2%2C2%2C3%2C-1%2C7%2C3%2C-2%2C1%2C9%29%29
Add -2*Row 1 to Row 2 to get the new Row 2

%28matrix%283%2C4%2C1%2C1%2C-1%2C2%2C0%2C1%2C1%2C3%2C3%2C-2%2C1%2C9%29%29

Add -3*Row 1 to Row 3 to get the new Row 3

%28matrix%283%2C4%2C1%2C1%2C-1%2C2%2C0%2C1%2C1%2C3%2C0%2C-5%2C4%2C3%29%29

Add 5*Row 2 to Row 3 to get the new Row 3

%28matrix%283%2C4%2C1%2C1%2C-1%2C2%2C0%2C1%2C1%2C3%2C0%2C0%2C9%2C18%29%29

Multiply Row 3 by 1%2F9 to make the pivot 1:

%28matrix%283%2C4%2C1%2C1%2C-1%2C2%2C0%2C1%2C1%2C3%2C0%2C0%2C1%2C2%29%29


Add -1*Row 3 to Row 2 to get the new Row 2

%28matrix%283%2C4%2C1%2C1%2C0%2C4%2C0%2C1%2C0%2C1%2C0%2C0%2C1%2C2%29%29


Add -1*Row 2 to Row 1 to get the new Row

%28matrix%283%2C4%2C1%2C0%2C0%2C3%2C0%2C1%2C0%2C1%2C0%2C0%2C1%2C2%29%29


The matrix is now in reduced row echelon form


If you need more help with row reduction or Gaussian elimination, check out The Linear Algebra Toolkit, and it will take you step-by-step through any Gaussian elimination problem.