The statement that “in computing the triangular factorization L n L n-1 …..L 1 A = U, fill in occurs in the jth column” means that Lj has a nonzero entry l ij where a ij = 0 or U has a nonzero entry...

The statement that “in computing the triangular factorization L_nL_n-1
…..L₁A = U, fill in occurs in the jth column” means that Lj has a nonzero entry l_ij
where a_ij
= 0 or U has a nonzero entry uij where a_ij
=0 Prove that fill in is  restricted to the spikes of A.