Decompose the following matrix into the product $LU$ using a compact format:
$$
\left[ \begin{array} {r r r} {{{2}}} & {{{-1}}} & {{{-1}}} \\ {{{-1}}} & {{{2}}} & {{{0}}} \\ {{{3}}} & {{{0}}} & {{{3}}} \\ \end{array} \right].
$$
The result is ____.

Options:
A. $$
L= \left[ \begin{matrix} {{1}} & {{0}} & {{0}} \\ {{-\frac{1} {3}}} & {{1}} & {{0}} \\ {{\frac{3} {2}}} & {{1}} & {{1}} \\ \end{matrix} \right],
$$
$$
U= \left[ \begin{matrix} {{{2}}} & {{{-1}}} & {{{-1}}} \\ {{{0}}} & {{{\frac{3} {2}}}} & {{{-\frac{2} {3}}}} \\ {{{0}}} & {{{0}}} & {{{5}}} \\ \end{matrix} \right]
$$
B. $$
L= \left[ \begin{matrix} {{1}} & {{0}} & {{0}} \\ {{-\frac{1} {4}}} & {{1}} & {{0}} \\ {{\frac{3} {2}}} & {{1}} & {{1}} \\ \end{matrix} \right],
$$
$$
U= \left[ \begin{matrix} {{{2}}} & {{{-1}}} & {{{-1}}} \\ {{{0}}} & {{{\frac{3} {4}}}} & {{{-\frac{1} {2}}}} \\ {{{0}}} & {{{0}}} & {{{5}}} \\ \end{matrix} \right]
$$
C. $$
L= \left[ \begin{matrix} {{1}} & {{0}} & {{0}} \\ {{-\frac{1} {2}}} & {{1}} & {{0}} \\ {{2}} & {{1}} & {{1}} \\ \end{matrix} \right],
$$
$$
U= \left[ \begin{matrix} {{{2}}} & {{{-1}}} & {{{-1}}} \\ {{{0}}} & {{{\frac{3} {2}}}} & {{{-\frac{1} {2}}}} \\ {{{0}}} & {{{0}}} & {{{5}}} \\ \end{matrix} \right]
$$
D. $$
L= \left[ \begin{matrix} {{1}} & {{0}} & {{0}} \\ {{0}} & {{1}} & {{0}} \\ {{\frac{3} {2}}} & {{1}} & {{1}} \\ \end{matrix} \right],
$$
$$
U= \left[ \begin{matrix} {{{2}}} & {{{-1}}} & {{{-1}}} \\ {{{0}}} & {{{\frac{3} {2}}}} & {{{-\frac{1} {2}}}} \\ {{{0}}} & {{{0}}} & {{{5}}} \\ \end{matrix} \right]
$$
E. $$
L= \left[ \begin{matrix} {{1}} & {{0}} & {{0}} \\ {{-\frac{1} {2}}} & {{1}} & {{0}} \\ {{\frac{3} {2}}} & {{1}} & {{1}} \\ \end{matrix} \right],
$$
$$
U= \left[ \begin{matrix} {{{2}}} & {{{-1}}} & {{{-1}}} \\ {{{0}}} & {{{\frac{3} {2}}}} & {{{-\frac{1} {2}}}} \\ {{{0}}} & {{{0}}} & {{{5}}} \\ \end{matrix} \right]
$$
F. $$
L= \left[ \begin{matrix} {{1}} & {{0}} & {{0}} \\ {{-\frac{1} {2}}} & {{1}} & {{0}} \\ {{\frac{3} {2}}} & {{1}} & {{1}} \\ \end{matrix} \right],
$$
$$
U= \left[ \begin{matrix} {{{2}}} & {{{-1}}} & {{{0}}} \\ {{{0}}} & {{{\frac{3} {2}}}} & {{{-\frac{1} {2}}}} \\ {{{0}}} & {{{0}}} & {{{5}}} \\ \end{matrix} \right]
$$
G. $$
L= \left[ \begin{matrix} {{1}} & {{0}} & {{0}} \\ {{-\frac{1} {2}}} & {{1}} & {{0}} \\ {{\frac{3} {2}}} & {{1}} & {{0}} \\ \end{matrix} \right],
$$
$$
U= \left[ \begin{matrix} {{{2}}} & {{{-1}}} & {{{-1}}} \\ {{{0}}} & {{{\frac{3} {2}}}} & {{{-\frac{1} {2}}}} \\ {{{0}}} & {{{0}}} & {{{5}}} \\ \end{matrix} \right]
$$
H. $$
L= \left[ \begin{matrix} {{1}} & {{0}} & {{0}} \\ {{-\frac{1} {2}}} & {{1}} & {{0}} \\ {{\frac{3} {2}}} & {{1}} & {{1}} \\ \end{matrix} \right],
$$
$$
U= \left[ \begin{matrix} {{{2}}} & {{{0}}} & {{{-1}}} \\ {{{0}}} & {{{\frac{3} {2}}}} & {{{-\frac{1} {2}}}} \\ {{{0}}} & {{{0}}} & {{{5}}} \\ \end{matrix} \right]
$$
I. $$
L= \left[ \begin{matrix} {{1}} & {{0}} & {{0}} \\ {{-\frac{1} {2}}} & {{1}} & {{0}} \\ {{\frac{3} {2}}} & {{\frac{1} {2}}} & {{1}} \\ \end{matrix} \right],
$$
$$
U= \left[ \begin{matrix} {{{2}}} & {{{-1}}} & {{{-1}}} \\ {{{0}}} & {{{\frac{3} {2}}}} & {{{-\frac{1} {2}}}} \\ {{{0}}} & {{{0}}} & {{{5}}} \\ \end{matrix} \right]
$$
J. $$
L= \left[ \begin{matrix} {{1}} & {{0}} & {{0}} \\ {{-\frac{1} {2}}} & {{1}} & {{0}} \\ {{\frac{3} {2}}} & {{0}} & {{1}} \\ \end{matrix} \right],
$$
$$
U= \left[ \begin{matrix} {{{2}}} & {{{-1}}} & {{{-1}}} \\ {{{0}}} & {{{\frac{3} {2}}}} & {{{-\frac{1} {2}}}} \\ {{{0}}} & {{{0}}} & {{{3}}} \\ \end{matrix} \right]
$$
Answer: E