The matrix \[\left[ {\text{A}} \right] = \left[ {\begin{array}{*{20}{c}} 2&1 \\ 4&{ - 1} \end{array}} \right]\]   is decomposed into a product of a lower triangular matrix x[L] and an upper triangular matrix [U]. The properly decomposed [L] and [U] matrices respectively are

A. \[\left[ {\begin{array}{*{20}{c}} 1&0 \\ 4&{ - 1} \end{array}} \right]{\text{ and }}\left[ {\begin{array}{*{20}{c}} 1&1 \\ 0&{ - 2} \end{array}} \right]\]

B. \[\left[ {\begin{array}{*{20}{c}} 2&0 \\ 4&{ - 1} \end{array}} \right]{\text{ and }}\left[ {\begin{array}{*{20}{c}} 1&1 \\ 0&1 \end{array}} \right]\]

C. \[\left[ {\begin{array}{*{20}{c}} 1&0 \\ 4&1 \end{array}} \right]{\text{ and }}\left[ {\begin{array}{*{20}{c}} 2&1 \\ 0&{ - 1} \end{array}} \right]\]

D. \[\left[ {\begin{array}{*{20}{c}} 2&0 \\ 4&{ - 3} \end{array}} \right]{\text{ and }}\left[ {\begin{array}{*{20}{c}} 1&{0.5} \\ 0&1 \end{array}} \right]\]

Answer: Option D