Row Reduction & Rank · Challenge problem

Elimination without row exchanges on a $4\times 4$ matrix $A$ used the multipliers $\ell_{21} = 2$, $\ell_{31} = 3$, $\ell_{32} = 4$, $\ell_{41} = 1$, $\ell_{42} = -1$, $\ell_{43} = 2$, so $A = LU$ with

Find the entry in row 4, column 1 of $L^{-1}$.