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Which of the following is the lower triangular part of a possible LU factorization of the matrix:

$$\begin{pmatrix}1&2\\\ 3&4\end{pmatrix}$$

A

$\begin{pmatrix}1&0\\\ 3&1\end{pmatrix}$

B

$\begin{pmatrix}-1&0\\\ 3&1\end{pmatrix}$

C

$\begin{pmatrix}1&0\\\ -3&1\end{pmatrix}$

D

$\begin{pmatrix}-1&0\\\ 3&-1\end{pmatrix}$

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