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Linear Algebra

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Moderate

Which is the Correct LU Factorization

LINALG-ESBSEM

Which of the following is an LU factorization of the matrix:

$$\begin{pmatrix}1&1&1\\\ 2&3&4\\\ -1&0&-1\end{pmatrix}$$

A

$\begin{pmatrix}1&0&0\\\ 4&1&0\\\ -1&-1&1\end{pmatrix}\begin{pmatrix}1&1&1\\\ 0&-1&-2\\\ 0&0&-2\end{pmatrix}$

B

$\begin{pmatrix}1&1&1\\\ 0&-1&-2\\\ 0&0&-2\end{pmatrix}\begin{pmatrix}1&0&0\\\ 4&1&0\\\ -1&-1&1\end{pmatrix}$

C

$\begin{pmatrix}1&0&0\\\ 2&1&0\\\ -1&1&1\end{pmatrix}\begin{pmatrix}1&1&1\\\ 0&1&2\\\ 0&0&-2\end{pmatrix}$

D

$\begin{pmatrix}1&1&1\\\ 0&1&2\\\ 0&0&-2\end{pmatrix}\begin{pmatrix}1&0&0\\\ 2&1&0\\\ -1&1&1\end{pmatrix}$