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Problem: Gauss Jordan Elimination inverse [[10,-9,-12],[7,-12,11],[-10,10,3]] [ Calculator, Method and examples ]

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``-9/10``-6/5``1/10``0``0`
`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``-57/10``97/5``-7/10``1``0`
`-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``1``-9``1``0``1`


`R_2 larr R_2xx-10/57`

 = 
`1``-9/10``-6/5``1/10``0``0`
`0``1``-194/57``7/57``-10/57``0`
`0``1``-9``1``0``1`


`R_1 larr R_1+9/10xx R_2`

 = 
`1``0``-81/19``4/19``-3/19``0`
`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``-319/57``50/57``10/57``1`


`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``1``-50/319``-10/319``-57/319`


`R_1 larr R_1+81/19xx R_3`

 = 
`1``0``0``-146/319``-93/319``-243/319`
`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``1``0``-425619/1036431``-292410/1036431``-194/319`
`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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