Solve this equation using the Gauss Jordan elimination method.
x + y - z = 7
x - y + 2z = 3
2x + y + z = 9
First, we rewrite the equations as an augmented matrix:
1 1 -1 | 7
1 -1 2 | 3
2 1 1 | 9
Now, we will perform row operations to simplify the matrix:
1 1 -1 | 7
0 -2 3 | -4
0 -1 3 | -5
1 1 -1 | 7
0 1.5 -2.25 | 2
0 -1 3 | -5
1 1 -1 | 7
0 1 -1.5 | 1
0 -1 3 | -5
Now, continue with row operations to get the matrix in reduced row-echelon form:
1 0 0 | 3
0 1 0 | 2
0 0 1 | -1
Therefore, the solution to the system of equations is x = 3, y = 2, z = -1.