Inverse of matrix using Gauss-Jordan Elimination method Example [[2,3,1],[0,5,6],[1,1,2]]

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

What's new

College Algebra

Games

Feedback

About us

Algebra

Matrix & Vector

Numerical Methods

Statistical Methods

Operation Research

Word Problems

Calculus

Geometry

Pre-Algebra

Home > Matrix & Vector calculators > Inverse of matrix using Gauss-Jordan Elimination method example

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

( Enter your problem )

Other related methods

Adjoint method
Gauss-Jordan Elimination method
Cayley Hamilton method

1. Example `[[3,1,1],[-1,2,1],[1,1,1]]`
(Previous example)

3. Example `[[2,3],[4,10]]`
(Next example)

2. Example `[[2,3,1],[0,5,6],[1,1,2]]`

2. Find Inverse of matrix using Gauss-Jordan Elimination method
`A=[[2,3,1],[0,5,6],[1,1,2]]`

Solution:
Given matrix is

`2`	`3`	`1`
`0`	`5`	`6`
`1`	`1`	`2`

Now finding inverse of the given matrix

`2`	`3`	`1`	`1`	`0`	`0`
`0`	`5`	`6`	`0`	`1`	`0`
`1`	`1`	`2`	`0`	`0`	`1`

`R_1 larr R_1-:2`

=

`1` `1=2-:2` `R_1 larr R_1-:2`	`3/2` `3/2=3-:2` `R_1 larr R_1-:2`	`1/2` `1/2=1-:2` `R_1 larr R_1-:2`	`1/2` `1/2=1-:2` `R_1 larr R_1-:2`	`0` `0=0-:2` `R_1 larr R_1-:2`	`0` `0=0-:2` `R_1 larr R_1-:2`
`0`	`5`	`6`	`0`	`1`	`0`
`1`	`1`	`2`	`0`	`0`	`1`

`R_3 larr R_3- R_1`

=

`1`	`3/2`	`1/2`	`1/2`	`0`	`0`
`0`	`5`	`6`	`0`	`1`	`0`
`0` `0=1-1` `R_3 larr R_3- R_1`	`-1/2` `-1/2=1-3/2` `R_3 larr R_3- R_1`	`3/2` `3/2=2-1/2` `R_3 larr R_3- R_1`	`-1/2` `-1/2=0-1/2` `R_3 larr R_3- R_1`	`0` `0=0-0` `R_3 larr R_3- R_1`	`1` `1=1-0` `R_3 larr R_3- R_1`

`R_2 larr R_2-:5`

=

`1`	`3/2`	`1/2`	`1/2`	`0`	`0`
`0` `0=0-:5` `R_2 larr R_2-:5`	`1` `1=5-:5` `R_2 larr R_2-:5`	`6/5` `6/5=6-:5` `R_2 larr R_2-:5`	`0` `0=0-:5` `R_2 larr R_2-:5`	`1/5` `1/5=1-:5` `R_2 larr R_2-:5`	`0` `0=0-:5` `R_2 larr R_2-:5`
`0`	`-1/2`	`3/2`	`-1/2`	`0`	`1`

`R_1 larr R_1-3/2xx R_2`

=

`1` `1=1-3/2xx0` `R_1 larr R_1-3/2xx R_2`	`0` `0=3/2-3/2xx1` `R_1 larr R_1-3/2xx R_2`	`-13/10` `-13/10=1/2-3/2xx6/5` `R_1 larr R_1-3/2xx R_2`	`1/2` `1/2=1/2-3/2xx0` `R_1 larr R_1-3/2xx R_2`	`-3/10` `-3/10=0-3/2xx1/5` `R_1 larr R_1-3/2xx R_2`	`0` `0=0-3/2xx0` `R_1 larr R_1-3/2xx R_2`
`0`	`1`	`6/5`	`0`	`1/5`	`0`
`0`	`-1/2`	`3/2`	`-1/2`	`0`	`1`

`R_3 larr R_3+1/2xx R_2`

=

`1`	`0`	`-13/10`	`1/2`	`-3/10`	`0`
`0`	`1`	`6/5`	`0`	`1/5`	`0`
`0` `0=0+1/2xx0` `R_3 larr R_3+1/2xx R_2`	`0` `0=-1/2+1/2xx1` `R_3 larr R_3+1/2xx R_2`	`21/10` `21/10=3/2+1/2xx6/5` `R_3 larr R_3+1/2xx R_2`	`-1/2` `-1/2=-1/2+1/2xx0` `R_3 larr R_3+1/2xx R_2`	`1/10` `1/10=0+1/2xx1/5` `R_3 larr R_3+1/2xx R_2`	`1` `1=1+1/2xx0` `R_3 larr R_3+1/2xx R_2`

`R_3 larr R_3xx10/21`

=

`1`	`0`	`-13/10`	`1/2`	`-3/10`	`0`
`0`	`1`	`6/5`	`0`	`1/5`	`0`
`0` `0=0xx10/21` `R_3 larr R_3xx10/21`	`0` `0=0xx10/21` `R_3 larr R_3xx10/21`	`1` `1=21/10xx10/21` `R_3 larr R_3xx10/21`	`-5/21` `-5/21=-1/2xx10/21` `R_3 larr R_3xx10/21`	`1/21` `1/21=1/10xx10/21` `R_3 larr R_3xx10/21`	`10/21` `10/21=1xx10/21` `R_3 larr R_3xx10/21`

`R_1 larr R_1+13/10xx R_3`

=

`1` `1=1+13/10xx0` `R_1 larr R_1+13/10xx R_3`	`0` `0=0+13/10xx0` `R_1 larr R_1+13/10xx R_3`	`0` `0=-13/10+13/10xx1` `R_1 larr R_1+13/10xx R_3`	`4/21` `4/21=1/2+13/10xx-5/21` `R_1 larr R_1+13/10xx R_3`	`-5/21` `-5/21=-3/10+13/10xx1/21` `R_1 larr R_1+13/10xx R_3`	`13/21` `13/21=0+13/10xx10/21` `R_1 larr R_1+13/10xx R_3`
`0`	`1`	`6/5`	`0`	`1/5`	`0`
`0`	`0`	`1`	`-5/21`	`1/21`	`10/21`

`R_2 larr R_2-6/5xx R_3`

=

`1`	`0`	`0`	`4/21`	`-5/21`	`13/21`
`0` `0=0-6/5xx0` `R_2 larr R_2-6/5xx R_3`	`1` `1=1-6/5xx0` `R_2 larr R_2-6/5xx R_3`	`0` `0=6/5-6/5xx1` `R_2 larr R_2-6/5xx R_3`	`2/7` `2/7=0-6/5xx-5/21` `R_2 larr R_2-6/5xx R_3`	`1/7` `1/7=1/5-6/5xx1/21` `R_2 larr R_2-6/5xx R_3`	`-4/7` `-4/7=0-6/5xx10/21` `R_2 larr R_2-6/5xx R_3`
`0`	`0`	`1`	`-5/21`	`1/21`	`10/21`

Solution By Gauss-Jordan Elimination method.
`[[4/21,-5/21,13/21],[2/7,1/7,-4/7],[-5/21,1/21,10/21]]`

This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then Submit Here