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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`

2. Example `2x+5y=16,3x+y=11`





Solve Equations 2x+5y=16,3x+y=11 using Gauss-Jordan Elimination method

Solution:
Total Equations are `2`

`2x+5y=16 -> (1)`

`3x+y=11 -> (2)`

Converting given equations into matrix form
`2``5``16`
`3``1``11`


`R_1 larr R_1-:2`

 = 
 `1` `1=2-:2`
`R_1 larr R_1-:2`
 `5/2` `5/2=5-:2`
`R_1 larr R_1-:2`
 `8` `8=16-:2`
`R_1 larr R_1-:2`
`3``1``11`


`R_2 larr R_2-3xx R_1`

 = 
`1``5/2``8`
 `0` `0=3-3xx1`
`R_2 larr R_2-3xx R_1`
 `-13/2` `-13/2=1-3xx5/2`
`R_2 larr R_2-3xx R_1`
 `-13` `-13=11-3xx8`
`R_2 larr R_2-3xx R_1`


`R_2 larr R_2xx-2/13`

 = 
`1``5/2``8`
 `0` `0=0xx-2/13`
`R_2 larr R_2xx-2/13`
 `1` `1=-13/2xx-2/13`
`R_2 larr R_2xx-2/13`
 `2` `2=-13xx-2/13`
`R_2 larr R_2xx-2/13`


`R_1 larr R_1-5/2xx R_2`

 = 
 `1` `1=1-5/2xx0`
`R_1 larr R_1-5/2xx R_2`
 `0` `0=5/2-5/2xx1`
`R_1 larr R_1-5/2xx R_2`
 `3` `3=8-5/2xx2`
`R_1 larr R_1-5/2xx R_2`
`0``1``2`


`i.e.`

`x=3`

`y=2`

Solution By Gauss jordan elimination method.
`x = 3`

`y = 2`




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