the matrix is applied twice followed by the vector b, the first matrix field becomes LR (stepwise)[br]beware of rounding errors...increase decimal places (15)[br][br]k - step to make zeros to collumn k [br]L - calculate the red formulas - make collumn k of L[br]R - calculate the black formulas - make lines k+1..n of R[br]k↕p - exchange line k-p[br]L R - generate new L,R matrices if n has changed[br]add vector b (= Ax) in TAB column 2n+1[br][br]Details and basics[br][url=https://www.geogebra.org/m/c94bmjuy]CAS LR Factorization Matrix Array[/url][math]\nwarrow[/math][br][br]Version[br][url=https://de.smath.com/cloud/sheet/PYns88HoM8]MathCad/SMath LU matrix array and row/column permutation vector[/url][math]\nearrow[/math]