A matrix P is decomposed into its symmetric part S and skew symmetric part V.

If \({\rm{S}} = \left( {\begin{array}{*{20}{c}} { - 4}&4&2\\ 4&3&{7/2}\\ 2&{7/2}&2 \end{array}} \right),{\rm{\;V}} = \left( {\begin{array}{*{20}{c}} 0&{ - 2}&3\\ 2&0&{7/2}\\ { - 3}&{ - 7/2}&0 \end{array}} \right)\)

then matrix P is

This question was previously asked in

PY 2: GATE ME 2020 Official Paper: Shift 2

Option 2 : \(\left( {\begin{array}{*{20}{c}}
{ - 4}&2&5\\
6&3&7\\
{ - 1}&0&2
\end{array}} \right)\)

CT 1: Ratio and Proportion

2672

10 Questions
16 Marks
30 Mins

__Concept:__

Every square matrix is expressed as the sum of symmetric and skew-symmetric matrix. Here, **S **is symmetric matrix and **V **is skew-symmetric matrix.

∴ P = S + V

__Calculation:__

\(P = \;\left[ {\begin{array}{*{20}{c}} { - 4}&4&2\\ 4&3&{\frac{7}{2}}\\ 2&{\frac{7}{2}}&2 \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 0&{ - 2}&3\\ 2&0&{\frac{7}{2}}\\ { - 3}&{ - \frac{7}{2}}&0 \end{array}} \right]\)

\(\therefore P = \;\left[ {\begin{array}{*{20}{c}} { - 4}&2&5\\ 6&3&7\\ { - 1}&0&2 \end{array}} \right]\)