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Find Gauss Jordan Elimination inverse [[10,-9,-12],[7,-12,11],[-10,10,3]]

Solution:
Your problem `->` Gauss Jordan Elimination inverse [[10,-9,-12],[7,-12,11],[-10,10,3]]


Given matrix is
`10``-9``-12`
`7``-12``11`
`-10``10``3`


Now finding inverse of the given matrix
`10``-9``-12``1``0``0`
`7``-12``11``0``1``0`
`-10``10``3``0``0``1`


`R_1 larr R_1-:10`

 = 
 `1` `1=10-:10`
`R_1 larr R_1-:10`
 `-9/10` `-9/10=-9-:10`
`R_1 larr R_1-:10`
 `-6/5` `-6/5=-12-:10`
`R_1 larr R_1-:10`
 `1/10` `1/10=1-:10`
`R_1 larr R_1-:10`
 `0` `0=0-:10`
`R_1 larr R_1-:10`
 `0` `0=0-:10`
`R_1 larr R_1-:10`
`7``-12``11``0``1``0`
`-10``10``3``0``0``1`


`R_2 larr R_2-7xx R_1`

 = 
`1``-9/10``-6/5``1/10``0``0`
 `0` `0=7-7xx1`
`R_2 larr R_2-7xx R_1`
 `-57/10` `-57/10=-12-7xx-9/10`
`R_2 larr R_2-7xx R_1`
 `97/5` `97/5=11-7xx-6/5`
`R_2 larr R_2-7xx R_1`
 `-7/10` `-7/10=0-7xx1/10`
`R_2 larr R_2-7xx R_1`
 `1` `1=1-7xx0`
`R_2 larr R_2-7xx R_1`
 `0` `0=0-7xx0`
`R_2 larr R_2-7xx R_1`
`-10``10``3``0``0``1`


`R_3 larr R_3+10xx R_1`

 = 
`1``-9/10``-6/5``1/10``0``0`
`0``-57/10``97/5``-7/10``1``0`
 `0` `0=-10+10xx1`
`R_3 larr R_3+10xx R_1`
 `1` `1=10+10xx-9/10`
`R_3 larr R_3+10xx R_1`
 `-9` `-9=3+10xx-6/5`
`R_3 larr R_3+10xx R_1`
 `1` `1=0+10xx1/10`
`R_3 larr R_3+10xx R_1`
 `0` `0=0+10xx0`
`R_3 larr R_3+10xx R_1`
 `1` `1=1+10xx0`
`R_3 larr R_3+10xx R_1`


`R_2 larr R_2xx-10/57`

 = 
`1``-9/10``-6/5``1/10``0``0`
 `0` `0=0xx-10/57`
`R_2 larr R_2xx-10/57`
 `1` `1=-57/10xx-10/57`
`R_2 larr R_2xx-10/57`
 `-194/57` `-194/57=97/5xx-10/57`
`R_2 larr R_2xx-10/57`
 `7/57` `7/57=-7/10xx-10/57`
`R_2 larr R_2xx-10/57`
 `-10/57` `-10/57=1xx-10/57`
`R_2 larr R_2xx-10/57`
 `0` `0=0xx-10/57`
`R_2 larr R_2xx-10/57`
`0``1``-9``1``0``1`


`R_1 larr R_1+9/10xx R_2`

 = 
 `1` `1=1+9/10xx0`
`R_1 larr R_1+9/10xx R_2`
 `0` `0=-9/10+9/10xx1`
`R_1 larr R_1+9/10xx R_2`
 `-81/19` `-81/19=-6/5+9/10xx-194/57`
`R_1 larr R_1+9/10xx R_2`
 `4/19` `4/19=1/10+9/10xx7/57`
`R_1 larr R_1+9/10xx R_2`
 `-3/19` `-3/19=0+9/10xx-10/57`
`R_1 larr R_1+9/10xx R_2`
 `0` `0=0+9/10xx0`
`R_1 larr R_1+9/10xx R_2`
`0``1``-194/57``7/57``-10/57``0`
`0``1``-9``1``0``1`


`R_3 larr R_3- R_2`

 = 
`1``0``-81/19``4/19``-3/19``0`
`0``1``-194/57``7/57``-10/57``0`
 `0` `0=0-0`
`R_3 larr R_3- R_2`
 `0` `0=1-1`
`R_3 larr R_3- R_2`
 `-319/57` `-319/57=-9--194/57`
`R_3 larr R_3- R_2`
 `50/57` `50/57=1-7/57`
`R_3 larr R_3- R_2`
 `10/57` `10/57=0--10/57`
`R_3 larr R_3- R_2`
 `1` `1=1-0`
`R_3 larr R_3- R_2`


`R_3 larr R_3xx-57/319`

 = 
`1``0``-81/19``4/19``-3/19``0`
`0``1``-194/57``7/57``-10/57``0`
 `0` `0=0xx-57/319`
`R_3 larr R_3xx-57/319`
 `0` `0=0xx-57/319`
`R_3 larr R_3xx-57/319`
 `1` `1=-319/57xx-57/319`
`R_3 larr R_3xx-57/319`
 `-50/319` `-50/319=50/57xx-57/319`
`R_3 larr R_3xx-57/319`
 `-10/319` `-10/319=10/57xx-57/319`
`R_3 larr R_3xx-57/319`
 `-57/319` `-57/319=1xx-57/319`
`R_3 larr R_3xx-57/319`


`R_1 larr R_1+81/19xx R_3`

 = 
 `1` `1=1+81/19xx0`
`R_1 larr R_1+81/19xx R_3`
 `0` `0=0+81/19xx0`
`R_1 larr R_1+81/19xx R_3`
 `0` `0=-81/19+81/19xx1`
`R_1 larr R_1+81/19xx R_3`
 `-146/319` `-146/319=4/19+81/19xx-50/319`
`R_1 larr R_1+81/19xx R_3`
 `-93/319` `-93/319=-3/19+81/19xx-10/319`
`R_1 larr R_1+81/19xx R_3`
 `-243/319` `-243/319=0+81/19xx-57/319`
`R_1 larr R_1+81/19xx R_3`
`0``1``-194/57``7/57``-10/57``0`
`0``0``1``-50/319``-10/319``-57/319`


`R_2 larr R_2+194/57xx R_3`

 = 
`1``0``0``-146/319``-93/319``-243/319`
 `0` `0=0+194/57xx0`
`R_2 larr R_2+194/57xx R_3`
 `1` `1=1+194/57xx0`
`R_2 larr R_2+194/57xx R_3`
 `0` `0=-194/57+194/57xx1`
`R_2 larr R_2+194/57xx R_3`
 `-425619/1036431` `-425619/1036431=7/57+194/57xx-50/319`
`R_2 larr R_2+194/57xx R_3`
 `-292410/1036431` `-292410/1036431=-10/57+194/57xx-10/319`
`R_2 larr R_2+194/57xx R_3`
 `-194/319` `-194/319=0+194/57xx-57/319`
`R_2 larr R_2+194/57xx R_3`
`0``0``1``-50/319``-10/319``-57/319`


Solution By Gauss Elimination Method.
`[[-146/319,-93/319,-243/319],[-425619/1036431,-292410/1036431,-194/319],[-50/319,-10/319,-57/319]]`






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