Pivots (Gaussian reduction)

[DrD]

Recognizing that Gauss Jordan elimination can be accomplished in many different ways, Gauss Jordan, LU decomposition would be dependent on the algorithm used to perform the reduction. With this in mind, check your results with that of Wolfram Alpha once again: LU(M2) from Wolfram Alpha. Specifically, notice that the diagonal of their upper triangular matrix U is [2,-8, 1], yet your decomposition is different. To check the results of the decomposition, L * U / P, should return the original M2 matrix, but in your case it doesn't. The permutation matrix shown, is not correct.

Another decomposition for LU(M2) is:

{[[1,0,0],[0.5,1,0],[−0.5,1,1]],[[4,−6,0],[0,4,1],[0,0,1]],[[0,1,0],[1,0,0],[0,0,1]]}, where the matrices are {L,U,P}. Checking: L*U/P ==M2.

There may be another update released before long, and hopefully resolve some of the issues.