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3. Gauss-Jordan Elimination method example ( Enter your problem )
  1. Example `2x+5y=21,x+2y=8`
  2. Example `2x+5y=16,3x+y=11`
  3. Example `2x+3y-z=5,3x+2y+z=10,x-5y+3z=0`
  4. Example `x+y+z=3,2x-y-z=3,x-y+z=9`

4. Example `x+y+z=3,2x-y-z=3,x-y+z=9`





Solve Equations x+y+z=3,2x-y-z=3,x-y+z=9 using Gauss-Jordan Elimination method

Solution:
Total Equations are `3`

`x+y+z=3 -> (1)`

`2x-y-z=3 -> (2)`

`x-y+z=9 -> (3)`

Converting given equations into matrix form
`1``1``1``3`
`2``-1``-1``3`
`1``-1``1``9`


`R_2 larr R_2-2xx R_1`

 = 
`1``1``1``3`
`0``-3``-3``-3`
`1``-1``1``9`


`R_3 larr R_3- R_1`

 = 
`1``1``1``3`
`0``-3``-3``-3`
`0``-2``0``6`


`R_2 larr R_2-:-3`

 = 
`1``1``1``3`
`0``1``1``1`
`0``-2``0``6`


`R_1 larr R_1- R_2`

 = 
`1``0``0``2`
`0``1``1``1`
`0``-2``0``6`


`R_3 larr R_3+2xx R_2`

 = 
`1``0``0``2`
`0``1``1``1`
`0``0``2``8`


`R_3 larr R_3-:2`

 = 
`1``0``0``2`
`0``1``1``1`
`0``0``1``4`


`R_2 larr R_2- R_3`

 = 
`1``0``0``2`
`0``1``0``-3`
`0``0``1``4`


`i.e.`

`x=2`

`y=-3`

`z=4`

Solution By Gauss jordan elimination method
`x=2,y=-3 and z=4`






This material is intended as a summary. Use your textbook for detail explanation.
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