Solving systems of linear equations using Gauss-Jordan Elimination method Example x+y+z=3,2x-y-z=3,x-y+z=9

We use cookies to improve your experience on our site and to show you relevant advertising. By browsing this website, you agree to our use of cookies. Learn more

Support us

Home > Matrix & Vector calculators > Solving systems of linear equations using Gauss-Jordan Elimination method example

3. Gauss-Jordan Elimination method example ( Enter your problem )

( Enter your problem )

Example `2x+5y=21,x+2y=8`
Example `2x+5y=16,3x+y=11`
Example `2x+3y-z=5,3x+2y+z=10,x-5y+3z=0`
Example `x+y+z=3,2x-y-z=3,x-y+z=9`

Other related methods

3. Example `2x+3y-z=5,3x+2y+z=10,x-5y+3z=0`
(Previous example)

4. Gauss Elimination Back Substitution method
(Next method)

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.
Any bug, improvement, feedback then Submit Here