Let
\(A=\left[\begin{matrix}2&3\\a&0\end{matrix}\right]\)
, \(a\in\mathbb{R}\) be written as \(P+Q\) where \(P\) is a symmetric matrix and \(Q\) is skew symmetric matrix. If \(\det(Q)=9\), then the modulus of the sum of all possible values of determinant of \(P\) is equal to :
\(A=\left[\begin{matrix}2&3\\a&0\end{matrix}\right]\)
, \(a\in\mathbb{R}\) be written as \(P+Q\) where \(P\) is a symmetric matrix and \(Q\) is skew symmetric matrix. If \(\det(Q)=9\), then the modulus of the sum of all possible values of determinant of \(P\) is equal to :
Show Hint
- 36
- 24
- 45
- 18
The Correct Option is A
Solution and Explanation
\(\det Q=\left(\frac{3-a}{2}\right)^2=9\Rightarrow(a-3)^2=36\Rightarrow a=9\) or \(a=-3\).
\(\det P=-\left(\frac{a+3}{2}\right)^2\). For \(a=9\): \(-36\). For \(a=-3\): \(0\).
Sum of possible values \(=-36\); its modulus is 36.
Answer: (1) 36
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