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 & Solution

Correct Answer: Option D

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The matrix left text A right = left begin array 20...

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

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