JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A=\left[\begin{array}{ll}2 & 3 \\ a & 0\end{array}\right], a \in R\) be written as \(P+Q\) where \(P\) is a symmetric matrix and \(Q\) is skew symmetric matrix. If \(\operatorname{det}(Q)=9\), then the modulus of the sum of all possible values of determinant of \(P\) is equal to:
- A \(24\)
- B \(18\)
- C \(45\)
- D \(36\)
Answer & Solution
Correct Answer
(D) \(36\)
Step-by-step Solution
Detailed explanation
\(A=\left[\begin{array}{ll}2 & 3 \\ a & 0\end{array}\right], a \in R\) and and \(P \frac{A+A^{T}}{2}=\left[\begin{array}{cc}2 & \frac{3+a}{2} \\ \frac{a+3}{2} & 0\end{array}\right]\) and…
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