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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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