Solution
= Solution
The elimination multipliers are $m_{21}=2$, $m_{31}=4$, and $m_{32}=3$. The unit <lower triangular matrix> in the <LU factorization> is therefore
$$
\boxed{L=\begin{pmatrix}1&0&0\\2&1&0\\4&3&1\end{pmatrix}.}
$$
Direct multiplication checks
$$
LU=\begin{pmatrix}2&1&1\\4&3&3\\8&7&9\end{pmatrix}=A.
$$
The positive signs in $L$ undo the row subtractions used during <Gaussian elimination>.