A method for finding a matrix inverse. To apply Gauss-Jordan elimination, operate on a matrix
[A I]=[a_(11) ... a_(1n) 1 0 ... 0; a_(21) ... a_(2n) 0 1 ... 0; | ... | | | ... |; a_(n1) ... a_(nn) 0 0 ... 1],
(1)

where I is the identity matrix, and use Gaussian elimination to obtain a matrix of the form
[1 0 ... 0 b_(11) ... b_(1n); 0 1 ... 0 b_(21) ... b_(2n); | | ... | | ... |; 0 0 ... 1 b_(n1) ... b_(nn)].
(2)

The matrix
B=[b_(11) ... b_(1n); b_(21) ... b_(2n); | ... |; b_(n1) ... b_(nn)]
(3)

is then the matrix inverse of A. The procedure is numerically unstable unless pivoting (exchanging rows and columns as appropriate) is used. Picking the largest available element as the pivot is usually a good choice.

SEE ALSO: Condensation, Gaussian Elimination, LU Decomposition, Matrix Equation