engineering recuitment AAI ATC Junior Executive 2025 Mock Test Series Mathematics Matrices Types of Matrices
If \(A = \left[ {\begin{array}{*{20}{c}} { - \;1}&5&1\\ 2&3&4\\ 7&0&9 \end{array}} \right] = \frac{1}{2} \cdot (P + Q)\) where P is symmetric and Q is skew symmetric matrix then P and Q are ?
1
\(P = \;\left[ {\begin{array}{*{20}{c}} { - \;2}&7&8\\ 7&6&4\\ 8&4&{18} \end{array}} \right]\;and\;Q = \;\left[ {\begin{array}{*{20}{c}} 0&3&{ - \;6}\\ { - \;3}&0&4\\ 6&{ - \;4}&0 \end{array}} \right]\)
2
\(P = \;\left[ {\begin{array}{*{20}{c}} { \;2}&7&8\\ 7&6&4\\ 8&4&{18} \end{array}} \right]\;and\;Q = \;\left[ {\begin{array}{*{20}{c}} 0&3&{ - \;6}\\ { - \;3}&0&4\\ 6&{ - \;4}&0 \end{array}} \right]\)
3
\(P = \;\left[ {\begin{array}{*{20}{c}} { - \;2}&7&8\\ 7&6&4\\ 8&4&{18} \end{array}} \right]\;and\;Q = \;\left[ {\begin{array}{*{20}{c}} 0&3&{ - \;6}\\ {\;3}&0&4\\ 6&{ - \;4}&0 \end{array}} \right]\)
4
\(P = \;\left[ {\begin{array}{*{20}{c}} { - \;2}&7&8\\ 7&6&4\\ 8&4&{18} \end{array}} \right]\;and\;Q = \;\left[ {\begin{array}{*{20}{c}} 0&3&{ - \;6}\\ {\;3}&0&4\\ 6&{\;4}&0 \end{array}} \right]\)