Linear AlgebraChallengeRow Reduction & Rank

Row Reduction & Rank · Challenge problem

Let $A$ be the symmetric Pascal matrix

A = \begin{pmatrix} 1 & 1 & 1 & 1 \\ 1 & 2 & 3 & 4 \\ 1 & 3 & 6 & 10 \\ 1 & 4 & 10 & 20 \end{pmatrix}.

Write $A = LU$ by elimination without row exchanges, with $1$ s on the diagonal of $L$ . What is $\ell_{43}$ ?