>Great. But don't you then use the factorization to determine the inverse of A (LAPACK example: call dgetrf to get the factorization, then call dgetri to comput

>Great. But don't you then use the factorization to determine the inverse of A (LAPACK example: call dgetrf to get the factorization, then call dgetri to compute the inverse using the factorization)? No. >How else would you solve Ax = b for x? Call dgetrs instead of dgetri. You use the factorisation directly (not the inverse) to get x from b. This is done by calling dgetrf to get the factorisation, then calling dgetrs to get the solution. You don't need to call dgetri. I'd do an example, but there are other replies to your comment that go through the mathematics.