I’ve put together an explanatory piece based on the context of (and its solution) from the Solution Manual for Jaan Kiusalaas’ Numerical Methods in Engineering with MATLAB , 2nd Edition.
[ P = \beginbmatrix 0 & 0 & 1 \ 1 & 0 & 0 \ 0 & 1 & 0 \endbmatrix, \quad L = \beginbmatrix 1 & 0 & 0 \ 0.6 & 1 & 0 \ -0.4 & 0.5455 & 1 \endbmatrix, \quad U = \beginbmatrix 5 & 2 & -3 \ 0 & -2.2 & 3.8 \ 0 & 0 & 4.2727 \endbmatrix ] I’ve put together an explanatory piece based on
The decomposition yields (as shown in manual): I’ve put together an explanatory piece based on