The GaussianElimination(A) command performs Gaussian elimination on the Matrix A and returns the upper triangular factor U with the same dimensions as A.

This command is equivalent to calling LUDecomposition with the output=['U'] option.

The ReducedRowEchelonForm(A) command performs Gauss-Jordan elimination on the Matrix A and returns the unique reduced row echelon form R of A.

This command is equivalent to calling LUDecomposition with the output=['R'] option.