Solve Equations 2x+3y-z=5,3x+2y+z=10,x-5y+3z=0 using Gauss-Jordan Elimination method

Solution:
Total Equations are `3`

`2x+3y-z=5 -> (1)`

`3x+2y+z=10 -> (2)`

`x-5y+3z=0 -> (3)`

Converting given equations into matrix form

	`2`	`3`	`-1`		`5`
	`3`	`2`	`1`		`10`
	`1`	`-5`	`3`		`0`

`R_1 larr R_1-:2`

=	`1` `1.5` `-0.5` `2.5` `3` `2` `1` `10` `1` `-5` `3` `0`

`R_2 larr R_2-3xx R_1`

=	`1` `1.5` `-0.5` `2.5` `0` `-2.5` `2.5` `2.5` `1` `-5` `3` `0`

`R_3 larr R_3- R_1`

=	`1` `1.5` `-0.5` `2.5` `0` `-2.5` `2.5` `2.5` `0` `-6.5` `3.5` `-2.5`

`R_2 larr R_2xx-0.4`

=	`1` `1.5` `-0.5` `2.5` `0` `1` `-1` `-1` `0` `-6.5` `3.5` `-2.5`

`R_1 larr R_1-1.5xx R_2`

=	`1` `0` `1` `4` `0` `1` `-1` `-1` `0` `-6.5` `3.5` `-2.5`

`R_3 larr R_3+6.5xx R_2`

=	`1` `0` `1` `4` `0` `1` `-1` `-1` `0` `0` `-3` `-9`

`R_3 larr R_3-:-3`

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

`R_1 larr R_1- R_3`

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

`R_2 larr R_2+ R_3`

=	`1` `0` `0` `1` `0` `1` `0` `2` `0` `0` `1` `3`

`i.e.`

`x=1`

`y=2`

`z=3`

Solution By Gauss jordan elimination method
`x=1,y=2 and z=3`

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