Use gauss-jordan elimination to solve the following linear system. –4x + 4y + 5z = 9 –2x + 2y + z = 3 –4x + 5y = 4

The system:
- 4 x + 4 y + 5 z = 9
- 2 x + 2 y + z = 3
- 4 x + 5 y = 4

Let`s take the 1st and the 2nd equation:
- 4 x + 4 y + 5 z = 8
- 2 x + 2 y + z = 3   / * ( - 2 )   / multiply both sides of equation by  - 2 . /

- 4 x + 4 y + 5 z = 9
+
  4 x - 4 y  -  2 z = - 6

                   3 z = 3   = >  z = 1
Then the 2nd and the 3rd equation:
- 2 x + 2 y = 3 - 1  /  * ( - 2 )
- 4 x + 5 y  =  4

   4 x  - 4 y = - 4
+
 - 4 x  + 5 y = 4

              y = 0
- 4 x + 5 * 0 = 4
 - 4 x = 4
    x = - 1
  x = - 1,  y = 0,  z = 1.