Dear expert, read this thoroughly before starting answering (I just lost one of my question because the last expert didn't). I have solved two questions with apparently contradictory statements / answers: Question 1) It says that A = LU is only possible when no pivots are equal to 0. 5. When zero appears in a pivot position, \( A=L U \) is not possible! (We need nonzero pivots \( d, f, i \) in \( U \).) Sho Question 2) The second matrix A, when decomposed, yields a U matrix with 0 in one of its pivots: 15. Find the \( P A=L D U \) factorizations (and check them) for \[ A=\left[\begin{array}{lll} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 2 & My question (this is the one, and only one, that I am asking to be answered): When a pivot is 0, is A = LU possible? A= 0 1 2 1 0 3 1 1 4 and A= 1 2 1 2 4 1 1 2 1
