1.

If A is a symmetric matrix and B is a skew-symmetric matrix such that \({\rm{A}} + {\rm{B}} = \left[ {\begin{array}{*{20}{c}} 2&3\\ 5&{ - 1} \end{array}} \right]\), then A and B are:

A. \(\left[ {\begin{array}{*{20}{c}} 2&{ 5}\\ { 5}&{ - 1} \end{array}} \right],\left[ {\begin{array}{*{20}{c}} 0&{ -1}\\ { 1}&{ 0} \end{array}} \right]\)
B. \(\left[ {\begin{array}{*{20}{c}} 2&{ 4}\\ { 4}&{ - 1} \end{array}} \right],\left[ {\begin{array}{*{20}{c}} 0&{ -1}\\ { 1}&{ 0} \end{array}} \right]\)
C. \(\left[ {\begin{array}{*{20}{c}} 1&{ 4}\\ { 4}&{ - 1} \end{array}} \right],\left[ {\begin{array}{*{20}{c}} 1&{ -1}\\ { 1}&{ 0} \end{array}} \right]\)
D. \(\left[ {\begin{array}{*{20}{c}} 2&{ 4}\\ { 4}&{ - 1} \end{array}} \right],\left[ {\begin{array}{*{20}{c}} 0&{ -1}\\ { 1}&{ 2} \end{array}} \right]\)
Answer» C. \(\left[ {\begin{array}{*{20}{c}} 1&{ 4}\\ { 4}&{ - 1} \end{array}} \right],\left[ {\begin{array}{*{20}{c}} 1&{ -1}\\ { 1}&{ 0} \end{array}} \right]\)


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